Vanishing nematic order beyond the pseudogap phase in overdoped cuprate superconductors

During the last decade, translational and rotational symmetry-breaking phases—density wave order and electronic nematicity—have been established as generic and distinct features of many correlated electron systems, including pnictide and cuprate superconductors. However, in cuprates, the relationship between these electronic symmetry-breaking phases and the enigmatic pseudogap phase remains unclear. Here, we employ resonant X-ray scattering in a cuprate high-temperature superconductor La1.6−xNd0.4SrxCuO4 (Nd-LSCO) to navigate the cuprate phase diagram, probing the relationship between electronic nematicity of the Cu 3d orbitals, charge order, and the pseudogap phase as a function of doping. We find evidence for a considerable decrease in electronic nematicity beyond the pseudogap phase, either by raising the temperature through the pseudogap onset temperature T* or increasing doping through the pseudogap critical point, p*. These results establish a clear link between electronic nematicity, the pseudogap, and its associated quantum criticality in overdoped cuprates. Our findings anticipate that electronic nematicity may play a larger role in understanding the cuprate phase diagram than previously recognized, possibly having a crucial role in the phenomenology of the pseudogap phase.

There is a growing realization that the essential physics of the cuprate high-temperature superconductors, and perhaps other strongly correlated materials, involves a rich interplay between different electronic symmetry-breaking phases (1–3) like superconductivity, spin or charge density wave (SDW or CDW) order (4–7), antiferromagnetism, electronic nematicity (8–14), and possibly other orders such as pair density wave order (15) or orbital current order (16).One or more of these orders may also be linked with the existence of a zero-temperature quantum critical point (QCP) in the superconducting state of the cuprates, similar to heavy-fermion, organic, pnictide, and iron-based superconductors (17–19). The significance of the QCP in describing the properties of the cuprates, as a generic organizing principle where quantum fluctuations in the vicinity of the QCP impact a wide swath of the cuprate phase diagram, remains an open question. Evidence for such a QCP and its influence include a linear in temperature resistivity extending to low temperature, strong mass enhancement via quantum oscillation studies (20), and an enhancement in the specific heat (21) in the field induced normal state, with some of the more-direct evidence for a QCP in the cuprates coming from measurements in the material La1.6−xNd0.4SrxCuO4 (Nd-LSCO). Moreover, the QCP also appears to be the endpoint of the pseudogap phase (21) that is marked, among other features, by transition of the electronic structure from small Fermi surface that is folded or truncated by the antiferromagnetic zone boundary in the pseudogap phase to a large Fermi surface at higher doping (22, 23) that is consistent with band structure calculations (24). However, in the cuprates, neither the QCP nor the change in the electronic structure have been definitively associated with a particular symmetry-breaking phase.In this article, we interrogate the possibility that the cuprates exhibit a connection between electronic nematic order, the pseudogap, and its associated QCP. In the pnictide superconductors, which are similar in many respects to the cuprates, electronic nematic order is more clearly established experimentally, and there have been reports of nematic fluctuations (25), non-Fermi liquid transport (26), and a change in the topology of the Fermi surface associated with a nematic QCP (27). Electronic nematicity refers to a breaking of rotational symmetry of the electronic structure in a manner that is not a straightforward result of crystalline symmetry, such that an additional electronic nematic order parameter beyond the structure would be required to describe the resulting phase. The manifestation of nematic order may therefore depend on the details of the crystal structure of the materials, such as whether the structure is tetragonal or orthorhombic. However, such a state can be difficult to identify in materials that have orthorhombic structures, which would naturally couple to any electronic nematic order and vice versa. Despite these challenges, experimental evidence for electronic nematic order that is distinct from the crystal structure include reports of electronic nematicity from bulk transport (8–10) and magnetometry measurements (11) in YBa2Cu3Oy (YBCO), scanning tunneling microscopy (STM) (13, 14, 28) in Bi2Sr2CaCu2O8+δ (Bi2212), inelastic neutron scattering (12) in YBCO, and resonant X-ray scattering (29) in (La,Nd,Ba,Sr,Eu)₂CuO₄. Moreover, STM studies in Bi2212 have reported intraunit cell nematicity disappearing around the pseudogap endpoint (30), which also seems to be a region of enhanced electronic nematic fluctuations (31, 32). In YBCO, there have also been reports of association between nematicity and the pseudogap onset temperature (9, 11).Here, we use resonant X-ray scattering to measure electronic nematic order in the cuprate Nd-LSCO as a function of doping and temperature to explore the relationship of electronic nematicity with the pseudogap phase. While evidence that a quantum critical point governs a wide swath of the phase diagram in hole-doped cuprates and is generic to many material systems remains unclear, investigation of Nd-LSCO provides the opportunity to probe the evolution of electronic nematicity over a wide range of doping in the same material system where some of the most compelling signatures of quantum criticality and electronic structure evolution have been observed. These include a divergence in the heat capacity (21), a change in the electronic structure from angle-dependent magnetoresistance (ADMR) measurements (24) in the vicinity of the QCP at x = 0.23, and the onset of the pseudogap (23). Our main result is that we observe a vanishing of the electronic nematic order in Nd-LSCO as hole doping is either increased above x = 0.23, which has been identified as the QCP doping for this system (21), or when temperature is increased above the pseudogap onset temperature T* (23). These observations indicate that electronic nematicity in Nd-LSCO is intimately linked to the pseudogap phase.     

Layering transitions and metastable structures of cholesteric liquid crystals in cylindrical confinement

Our study of cholesteric lyotropic chromonic liquid crystals in cylindrical confinement reveals the topological aspects of cholesteric liquid crystals. The double-twist configurations we observe exhibit discontinuous layering transitions, domain formation, metastability, and chiral point defects as the concentration of chiral dopant is varied. We demonstrate that these distinct layer states can be distinguished by chiral topological invariants. We show that changes in the layer structure give rise to a chiral soliton similar to a toron, comprising a metastable pair of chiral point defects. Through the applicability of the invariants we describe to general systems, our work has broad relevance to the study of chiral materials.

Chiral liquid crystals (LCs) are ubiquitous, useful, and rich systems (1–4). From the first discovery of the liquid crystalline phase to the variety of chiral structures formed by biomolecules (5–9), the twisted structure, breaking both mirror and continuous spatial symmetries, is omnipresent. The unique structure also makes the chiral nematic (cholesteric) LC, an essential material for applications utilizing the tunable, responsive, and periodic modulation of anisotropic properties.The cholesteric is also a popular model system to study the geometry and topology of partially ordered matter. The twisted ground state of the cholesteric is often incompatible with confinement and external fields, exhibiting a large variety of frustrated and metastable director configurations accompanying topological defects. Besides the classic example of cholesterics in a Grandjean−Cano wedge (10, 11), examples include cholesteric droplets (12–16), colloids (17–19), shells (20–22), tori (23, 24), cylinders (25–29), microfabricated structures (30, 31), and films between parallel plates with external fields (32–40). These structures are typically understood using a combination of nematic (achiral) topology (41, 42) and energetic arguments, for example, the highly successful Landau−de Gennes approach (43). However, traditional extensions of the nematic topological approach to cholesterics are known to be conceptually incomplete and difficult to apply in regimes where the system size is comparable to the cholesteric pitch (41, 44).An alternative perspective, chiral topology, can give a deeper understanding of these structures (45–47). In this approach, the key role is played by the twist density, given in terms of the director field n by n⋅∇×n. This choice is not arbitrary; the Frank free energy prefers n⋅∇×n≈−q0=2π/p0 with a helical pitch p0, and, from a geometric perspective, n⋅∇×n≠0 defines a contact structure (48). This allows a number of new integer-valued invariants of chiral textures to be defined (45). A configuration with a single sign of twist is chiral, and two configurations which cannot be connected by a path of chiral configurations are chirally distinct, and hence separated by a chiral energy barrier. Within each chiral class of configuration, additional topological invariants may be defined using methods of contact topology (45–48), such as layer numbers. Changing these chiral topological invariants requires passing through a nonchiral configuration. Cholesterics serve as model systems for the exploration of chirality in ordered media, and the phenomena we describe here—metastability in chiral systems controlled by chiral topological invariants—has applicability to chiral order generally. This, in particular, includes chiral ferromagnets, where, for example, our results on chiral topological invariants apply to highly twisted nontopological Skyrmions (49, 50) (“Skyrmionium”).Our experimental model to explore the chiral topological invariants is the cholesteric phase of lyotropic chromonic LCs (LCLCs). The majority of experimental systems hitherto studied are based on thermotropic LCs with typical elastic and surface-anchoring properties. The aqueous LCLCs exhibiting unusual elastic properties, that is, very small twist modulus K2 and large saddle-splay modulus K24 (51–56), often leading to chiral symmetry breaking of confined achiral LCLCs (53, 54, 56–61), may enable us to access uncharted configurations and defects of topological interests. For instance, in the layer configuration by cholesteric LCLCs doped with chiral molecules, their small K2 provides energetic flexibility to the thickness of the cholesteric layer, that is, the repeating structure where the director n twists by π. The large K24 affords curvature-induced surface interactions in combination with a weak anchoring strength of the lyotropic LCs (62–64).We present a systematic investigation of the director configuration of cholesteric LCLCs confined in cylinders with degenerate planar anchoring, depending on the chiral dopant concentration. We show that the structure of cholesteric configurations is controlled by higher-order chiral topological invariants. We focus on two intriguing phenomena observed in cylindrically confined cholesterics. First, the cylindrical symmetry renders multiple local minima to the energy landscape and induces discontinuous increase of twist angles, that is, a layering transition, upon the dopant concentration increase. Additionally, the director configurations of local minima coexist as metastable domains with point-like defects between them. We demonstrate that a chiral layer number invariant distinguishes these configurations, protects the distinct layer configurations (45), and explains the existence of the topological defect where the invariant changes.     

Optimized river diversion scenarios promote sustainability of urbanized deltas

Socioeconomic viability of fluvial-deltaic systems is limited by natural processes of these dynamic landforms. An especially impactful occurrence is avulsion, whereby channels unpredictably shift course. We construct a numerical model to simulate artificial diversions, which are engineered to prevent channel avulsion, and direct sediment-laden water to the coastline, thus mitigating land loss. We provide a framework that identifies the optimal balance between river diversion cost and civil disruption by flooding. Diversions near the river outlet are not sustainable, because they neither reduce avulsion frequency nor effectively deliver sediment to the coast; alternatively, diversions located halfway to the delta apex maximize landscape stability while minimizing costs. We determine that delta urbanization generates a positive feedback: infrastructure development justifies sustainability and enhanced landform preservation vis-à-vis diversions.

Deltaic environments are critical for societal wellbeing because these landscapes provide an abundance of natural resources that promote human welfare (1, 2). However, the sustainability of deltas is uncertain due to sea-level rise (3, 4), sediment supply reduction (4–6), and land subsidence (7, 8). Additionally, river avulsion, the process of sudden channel relocation (9, 10), presents a dichotomy to delta sustainability: the unanticipated civil disruption associated with flooding brought by channel displacement is at odds with society’s desire for landscape stability, yet channel relocation is needed to deliver nutrients and sediment to various locations along the deltaic coastline (11, 12). Indeed, for many of the world’s megadeltas, channel engineering practices have sought to restrict channel mobility and limit floodplain connectivity (13, 14), which in turn prevents sediment dispersal that is necessary to sustain deltas; as a consequence, land loss has ensued (15). Despite providing near-term stability (13–15), engineering of deltaic channels is a long-term detrimental practice (11, 15–17).To maximize societal benefit, measures that promote delta sustainability must balance engineering infrastructure cost and impact on delta morphology with benefits afforded by maintaining and developing deltaic landscapes (1, 2, 11, 12, 16–19). For example, channel diversions, costing millions to billions of dollars (20–22), are now planned worldwide to both prevent unintended avulsions and ensure coastal sustainability through enhanced sediment delivery (e.g., Fig. 1A) (20, 21, 23–26).Open in a separate windowFig. 1.(A) Satellite image of Yellow River delta (Landsat, 1978) showing coastline response to a diversion in 1976 at the open circle, which changed the channel course from the north (Diaokou lobe) to the east (Qingshuigou lobe) and produced flooding over the stripe-hatched area (30). (B and C) Planform view (B) and along-channel cross-section view (C) of conceptual model for numerical simulations and societal benefit formulation. In the diagrams, a diversion at LD≈0.8Lb floods an area (af) defined by Lf and θ, diverting sediment away from the deltaic lobe (with length Ll). Aggradation of the former channel bed (dashed line) is variable; hence, diversion length influences the propensity for subsequent avulsion setup.In this article, we consider the benefits and costs of such engineered river diversions and determine how these practices most effectively sustain deltaic landscapes, by assessing optimal placement and timing for river diversions. Addressing these points requires combining two modeling frameworks: a morphodynamic approach—evolving the landscape over time and space by evaluating the interactions of river fluid flow and sediment transport—and a decision-making framework (21, 22, 27, 28). The former simulates deltaic channel diversions by assessing the nonlinear relationships between channel diversion length (LD) and the frequency (timing) of avulsions (TA), while the latter incorporates a societal benefit model that approximates urbanization by considering the cost of flooding a landscape that would otherwise generate revenue. The aim is to optimize timing and placement of channel diversions, by giving consideration to morphodynamic operations and societal wellbeing. Interestingly, optimal societal benefit indicates that urbanization justifies enhanced sustainability measures, which contradicts existing paradigms that label development and sustainability mutually exclusive (3, 7, 12). Ultimately, the societal benefit model should be an integrated component in decision-making frameworks. This will help locate diversions and promote sustainable and equitable decisions considering historical, ethical, and environmental contexts for river management decisions (29).     

Nature of dynamic gradients,glass formation,and collective effects in ultrathin freestanding films

Molecular, polymeric, colloidal, and other classes of liquids can exhibit very large, spatially heterogeneous alterations of their dynamics and glass transition temperature when confined to nanoscale domains. Considerable progress has been made in understanding the related problem of near-interface relaxation and diffusion in thick films. However, the origin of “nanoconfinement effects” on the glassy dynamics of thin films, where gradients from different interfaces interact and genuine collective finite size effects may emerge, remains a longstanding open question. Here, we combine molecular dynamics simulations, probing 5 decades of relaxation, and the Elastically Cooperative Nonlinear Langevin Equation (ECNLE) theory, addressing 14 decades in timescale, to establish a microscopic and mechanistic understanding of the key features of altered dynamics in freestanding films spanning the full range from ultrathin to thick films. Simulations and theory are in qualitative and near-quantitative agreement without use of any adjustable parameters. For films of intermediate thickness, the dynamical behavior is well predicted to leading order using a simple linear superposition of thick-film exponential barrier gradients, including a remarkable suppression and flattening of various dynamical gradients in thin films. However, in sufficiently thin films the superposition approximation breaks down due to the emergence of genuine finite size confinement effects. ECNLE theory extended to treat thin films captures the phenomenology found in simulation, without invocation of any critical-like phenomena, on the basis of interface-nucleated gradients of local caging constraints, combined with interfacial and finite size-induced alterations of the collective elastic component of the structural relaxation process.

Spatially heterogeneous dynamics in glass-forming liquids confined to nanoscale domains (1–7) play a major role in determining the properties of molecular, polymeric, colloidal, and other glass-forming materials (8), including thin films of polymers (9, 10) and small molecules (11–15), small-molecule liquids in porous media (2, 4, 16, 17), semicrystalline polymers (18, 19), polymer nanocomposites (20–22), ionomers (23–25), self-assembled block and layered (26–33) copolymers, and vapor-deposited ultrastable molecular glasses (34–36). Intense interest in this problem over the last 30 y has also been motivated by the expectation that its understanding could reveal key insights concerning the mechanism of the bulk glass transition.Considerable progress has been made for near-interface altered dynamics in thick films, as recently critically reviewed (1). Large amplitude gradients of the structural relaxation time, τ(z,T), converge to the bulk value, τ_bulk(T), in an intriguing double-exponential manner with distance, z, from a solid or vapor interface (13, 37–42). This implies that the corresponding effective activation barrier, F_total(z,T,H) (where H is film thickness), varies exponentially with z, as does the glass transition temperature, T_g (37). Thus the fractional reduction in activation barrier, ε(z,H), obeys the equation ε(z,H)≡1−Ftotal(z,T,H)/Ftotal,bulk(T)=ε0⁡exp(−z/ξF), where F_total,bulk(T) is the bulk temperature-dependent barrier and ξ_F a length scale of modest magnitude. Although the gradient of reduction in absolute activation barriers becomes stronger with cooling, the amplitude of the fractional reduction of the barrier gradient, quantified by ε₀, and the range ξ_F of this gradient, exhibit a weak or absent temperature dependence at the lowest temperatures accessed by simulations (typically with the strength of temperature dependence of ξ_F decreasing rather than increasing on cooling), which extend to relaxation timescales of order 10⁵ ps. This finding raises questions regarding the relevance of critical-phenomena–like ideas for nanoconfinement effects (1). Partially due to this temperature invariance, coarse-grained and all-atom simulations (1, 37, 42, 43) have found a striking empirical fractional power law decoupling relation between τ(z,T) and τ_bulk(T):τ(T,z)τbulk(T)∝(τbulk(T))−ε(z).[1]Recent theoretical analysis suggests (44) that this behavior is consistent with a number of experimental data sets as well (45, 46). Eq. 1 also corresponds to a remarkable factorization of the temperature and spatial location dependences of the barrier:Ftotal(z,T)=[1−ε(z)]Ftotal,bulk(T).[2]This finding indicates that the activation barrier for near-interface relaxation can be factored into two contributions: a z-dependent, but T-independent, “decoupling exponent,” ε(z), and a temperature-dependent, but position-insensitive, bulk activation barrier, F_total,bulk(T). Eq. 2 further emphasizes that ε(z) is equivalent to an effective fractional barrier reduction factor (for a vapor interface), 1−Ftotal(z,T,H)/Ftotal,bulk(T), that can be extracted from relaxation data.In contrast, the origin of “nanoconfinement effects” in thin films, and how much of the rich thick-film physics survives when dynamic gradients from two interfaces overlap, is not well understood. The distinct theoretical efforts for aspects of the thick-film phenomenology (44, 47–50) mostly assume an additive summation of one-interface effects in thin films, thereby ignoring possibly crucial cooperative and whole film finite size confinement effects. If the latter involve phase-transition–like physics as per recent speculations (14, 51), one can ask the following: do new length scales emerge that might be truncated by finite film size? Alternatively, does ultrathin film phenomenology arise from a combination of two-interface superposition of the thick-film gradient physics and noncritical cooperative effects, perhaps in a property-, temperature-, and/or thickness-dependent manner?Here, we answer these questions and establish a mechanistic understanding of thin-film dynamics for the simplest and most universal case: a symmetric freestanding film with two vapor interfaces. We focus on small molecules (modeled theoretically as spheres) and low to medium molecular weight unentangled polymers, which empirically exhibit quite similar alterations in dynamics under “nanoconfinement.” We do not address anomalous phenomena [e.g., much longer gradient ranges (29), sporadic observation of two distinct glass transition temperatures (52, 53)] that are sometimes reported in experiments with very high molecular weight polymers and which may be associated with poorly understood chain connectivity effects that are distinct from general glass formation physics (54–56).We employ a combination of molecular dynamics simulations with a zero-parameter extension to thin films of the Elastically Cooperative Nonlinear Langevin Equation (ECNLE) theory (57, 58). This theory has previously been shown to predict well both bulk activated relaxation over up to 14 decades (44–46) and the full single-gradient phenomenology in thick films (1). Here, we extend this theory to treat films of finite thickness, accounting for coupled interface and geometric confinement effects. We compare predictions of ECNLE theory to our previously reported (37, 43) and new simulations, which focus on translational dynamics of films comprised of a standard Kremer–Grest-like bead-spring polymer model (see SI Appendix). These simulations cover a wide range of film thicknesses (H, from 4 to over 90 segment diameters σ) and extend to low temperatures where the bulk alpha time is ∼0.1 μs (10⁵ Lennard Jones time units τ_LJ).The generalized ECNLE theory is found to be in agreement with simulation for all levels of nanoconfinement. We emphasize that this theory does not a priori assume any of the empirically established behaviors discovered using simulation (e.g., fractional power law decoupling, double-exponential barrier gradient, gradient flattening) but rather predicts these phenomena based upon interfacial modifications of the two coupled contributions to the underlying activation barrier– local caging constraints and a long-ranged collective elastic field. It is notable that this strong agreement is found despite the fact the dynamical ideas are approximate, and a simple hard sphere fluid model is employed in contrast to the bead-spring polymers employed in simulation. The basic unit of length in simulation (bead size σ) and theory (hard sphere diameter d) are expected to be proportional to within a prefactor of order unity, which we neglect in making comparisons.As an empirical matter, we find from simulation that many features of thin-film behavior can be described to leading order by a linear superposition of the thick-film gradients in activation barrier, that is:ε(z,H)=1−Ftotal(z,T,H)/Ftotal,bulk(T)≈ε0[exp(−z/ξF)+exp(−(H−z)/ξF)],[3]where the intrinsic decay length ξ_F is unaltered from its thick-film value and where ε₀ is a constant that, in the hypothesis of literal gradient additivity, is invariant to temperature and film thickness. We employ this functional form [originally suggested by Binder and coworkers (59)], which is based on a simple superposition of the two single-interface gradients, as a null hypothesis throughout this study: this form is what one expects if no new finite-size physics enters the thin-film problem relative to the thick film.However, we find that the superposition approximation progressively breaks down, and eventually entirely fails, in ultrathin films as a consequence of the emergence of a finite size confinement effect. The ECNLE theory predicts that this failure is not tied to a phase-transition–like mechanism but rather is a consequence of two key coupled physical effects: 1) transfer of surface-induced reduction of local caging constraints into the film, and 2) interfacial truncation and nonadditive modifications of the collective elastic contribution to the activation barrier.     

Transient conformational fluctuation of TePixD during a reaction

Knowledge of the dynamical behavior of proteins, and in particular their conformational fluctuations, is essential to understanding the mechanisms underlying their reactions. Here, transient enhancement of the isothermal partial molar compressibility, which is directly related to the conformational fluctuation, during a chemical reaction of a blue light sensor protein from the thermophilic cyanobacterium Thermosynechococcus elongatus BP-1 (TePixD, Tll0078) was investigated in a time-resolved manner. The UV-Vis absorption spectrum of TePixD did not change with the application of high pressure. Conversely, the transient grating signal intensities representing the volume change depended significantly on the pressure. This result implies that the compressibility changes during the reaction. From the pressure dependence of the amplitude, the compressibility change of two short-lived intermediate (I₁ and I₂) states were determined to be +(5.6 ± 0.6) × 10⁻² cm³⋅mol⁻¹⋅MPa⁻¹ for I₁ and +(6.6 ± 0.7)×10⁻² cm³⋅mol⁻¹⋅MPa⁻¹ for I₂. This result showed that the structural fluctuation of intermediates was enhanced during the reaction. To clarify the relationship between the fluctuation and the reaction, the compressibility of multiply excited TePixD was investigated. The isothermal compressibility of I₁ and I₂ intermediates of TePixD showed a monotonic decrease with increasing excitation laser power, and this tendency correlated with the reactivity of the protein. This result indicates that the TePixD decamer cannot react when its structural fluctuation is small. We concluded that the enhanced compressibility is an important factor for triggering the reaction of TePixD. To our knowledge, this is the first report showing enhanced fluctuations of intermediate species during a protein reaction, supporting the importance of fluctuations.Proteins often transfer information through changes in domain–domain (or intermolecular) interactions. Photosensor proteins are an important example. They have light-sensing domains and function by using the light-driven changes in domain–domain interactions (1). The sensor of blue light using FAD (BLUF) domain is a light-sensing module found widely among the bacterial kingdom (2). The BLUF domain initiates its photoreaction by the light excitation of the flavin moiety inside the protein, which changes the domain–domain interaction, causing a quaternary structural change and finally transmitting biological signals (3, 4). It has been an important research topic to elucidate how the initial photochemistry occurring in the vicinity of the chromophore leads to the subsequent large conformation change in other domains, which are generally apart from the chromophore.It may be reasonable to consider that the conformation change in the BLUF domain is the driving force in its subsequent reaction; that is, the change in domain–domain interaction. However, sometimes, clear conformational changes have not been observed for the BLUF domain; its conformation is very similar before and after photo-excitation (5–13). The circular dichroism (CD) spectra of BLUF proteins AppA and PixD from thermophilic cyanobacterium Thermosynechococcus elongatus BP-1 (TePixD) did not change on illumination (5, 13). Similarly, solution NMR studies of AppA and BlrB showed only small chemical shifts on excitation (9, 10). The solution NMR structure of BlrP1 showed a clear change, but this was limited in its C-terminal extension region and not core BLUF (11). Furthermore, the diffusion coefficient (D) of the BLUF domain of YcgF was not changed by photo-excitation (12), although D is sensitive to global conformational changes. These results imply that a minor structural change occurs in the BLUF domain. In such cases, how does the BLUF domain control its interdomain interaction? Recently, a molecular dynamics (MD) simulation on another light-sensing domain, the light-oxygen-voltage (LOV) sensing domain, suggested that fluctuation of the LOV core structure could be a key to understanding the mechanism of information transfer (14–16).Because proteins work at room temperature, they are exposed to thermal fluctuations. The importance of such structural fluctuations for biomolecular reactions has been also pointed out: for example, enzymatic activity (17–20). Experimental detections of such conformation fluctuations using single molecular detection (21) or NMR techniques such as the hydrogen-deuterium (H-D) exchange, relaxation dispersion method, and high-pressure NMR (22–24) have succeeded. However, these techniques could not detect the fluctuation of short-lived transient species. Indeed, single molecule spectroscopy can trace the fluctuation in real time, but it is still rather difficult to detect rapid fluctuations for a short-lived intermediate during a reaction. Therefore, information about the fluctuation of intermediates is thus far limited.A thermodynamic measurement is another way to characterize the fluctuation of proteins. In particular, the partial molar isothermal compressibility [K¯T=−(∂V¯/∂P)T] is essential, because this property is directly linked to the mean-square fluctuations of the protein partial molar volume by 〈(V¯−〈V¯〉)2〉≡〈δV¯2〉=kBTK¯T (25). (Here, <X> means the averaged value of a quantity of X.) Therefore, isothermal compressibility is thought to reflect the structural fluctuation of molecules (26). However, experimental measurement of this parameter of proteins in a dilute solution is quite difficult. Indeed, this quantity has been determined indirectly from the theoretical equation using the adiabatic compressibility of a protein solution, which was determined by the sound velocity in the solution (26–31). Although the relation between volume fluctuations and isothermal compressibility is rigorously correct only with respect to the intrinsic part of the volume compressibility, and not the partial molar volume compressibility (32), we considered that this partial molar volume compressibility is still useful for characterizing the fluctuation of the protein structure including its interacting water molecules. In fact, the relationship between β¯T and the volume fluctuation has been often used to discuss the fluctuation of proteins (17, 26–28), and the strong correlation of β¯T of reactants with the functioning for some enzymes (17, 33, 34) has been reported. These studies show the functional importance of the structural fluctuation represented by β¯T. However, thermodynamic techniques lack time resolution, and it has been impossible to measure the fluctuations of short-lived intermediate species.Recently, we developed a time-resolving method for assessing thermodynamic properties using the pulsed laser induced transient grating (TG) method. Using this method, we thus far succeeded in measuring the enthalpy change (ΔH) (35–38), partial molar volume change (ΔV¯) (12, 35, 37), thermal expansion change (Δα¯th) (12, 37), and heat capacity change (ΔC_p) (36–38) for short-lived species. Therefore, in principle, the partial molar isothermal compressibility change (ΔK¯T) of a short-lived intermediate become observable if we conduct the TG experiment under the high-pressure condition and detect ΔV¯ with varying external pressure.There are several difficulties in applying the traditional high-pressure cell to the TG method to measure thermodynamic parameters quantitatively. The most serious problem is ensuring the quantitative performance of the intensity of TG signals measured under the high-pressure condition. On this point, our group has developed a new high-pressure cell specially designed for TG spectroscopy (39) and overcome this problem. In this paper, by applying this high-pressure TG system to the BLUF protein TePixD, we report the first measurement, to our knowledge, of ΔK¯T of short-lived intermediates to investigate the mechanism underlying signal transmission by BLUF proteins, from the view point of the transient fluctuation.TePixD is a homolog of the BLUF protein PixD, which regulates the phototaxis of cyanobacterium (40) and exists in a thermophilic cyanobacterium Thermocynechococcus elongates BP-1 (Tll0078). TePixD is a relatively small (17 kDa) protein that consists only of the BLUF domain with two extended helices in the C-terminal region. In crystals and solutions, it forms a decamer that consists of two pentameric rings (41). The photochemistry of TePixD is typical among BLUF proteins (42–45); on blue light illumination, the absorption spectrum shifts toward red by about 10 nm within a nanosecond. The absorption spectrum does not change further, and the dark state is recovered with a time constant of ∼5 s at room temperature (40, 43). The spectral red shift was explained by the rearrangement of the hydrogen bond network around the chromophore (6, 46–48). The TG method has revealed the dynamic photoreaction mechanism, which cannot be detected by conventional spectroscopic methods. The TG signal of TePixD (Fig. S1) showed that there are two spectrally silent reaction phases: a partial molar volume expansion with the time constant of ∼40 μs and the diffusion coefficient (D) change with a time constant of ∼4 ms. Furthermore, it was reported that the pentamer and decamer states of TePixD are in equilibrium and that the final photoproduct of the decamer is pentamers generated by its dissociation (13, 49). On the basis of these studies, the reaction scheme has been identified as shown in Fig. 1. Here, I₁ is the intermediate of the spectrally red-shifted species (generated within a nanosecond) and I₂ is the one created on the subsequent volume expansion process of +4 cm³⋅mol⁻¹ (∼40 μs). Furthermore, an experiment of the excitation laser power dependence of its TG signal revealed that the TePixD decamer undergoes the original dissociation reaction when only one monomer in the decamer is excited (50). In this study, we investigated the transient compressibility of the intermediates I₁ and I₂ of the photoreaction of TePixD and found a direct link between their fluctuation and reactivity.Open in a separate windowFig. 1.Schematic illustration of the photoreaction of TePixD. Yellow circles represent the TePixD monomer in the ground state, which constructs the decamer and pentamer states. In the dark state, these two forms are in equilibrium. The excited, spectral red-shifted state of the TePixD monomer is indicated by a red circle. The square represents the I₂ state of the monomer, which is created by the volume expansion process.     

Giant vacuum forces via transmission lines

Quantum electromagnetic fluctuations induce forces between neutral particles, known as the van der Waals and Casimir interactions. These fundamental forces, mediated by virtual photons from the vacuum, play an important role in basic physics and chemistry and in emerging technologies involving, e.g., microelectromechanical systems or quantum information processing. Here we show that these interactions can be enhanced by many orders of magnitude upon changing the character of the mediating vacuum modes. By considering two polarizable particles in the vicinity of any standard electric transmission line, along which photons can propagate in one dimension, we find a much stronger and longer-range interaction than in free space. This enhancement may have profound implications on many-particle and bulk systems and impact the quantum technologies mentioned above. The predicted giant vacuum force is estimated to be measurable in a coplanar waveguide line.The seminal works of London (1), Casimir and Polder (2), and Casimir (3) identified quantum electromagnetic fluctuations to be the source of both short-range [van der Waals (vdW)] and retarded, long-range (Casimir) interactions between polarizable objects, which may be viewed as an exchange of virtual photons from the vacuum. Subsequent studies of these interactions (4–14) revealed their modifications, such as retardation and nonadditivity (15), brought about by the geometry of the polarizable objects. The ability to design these interactions is important for their possible use and exploration in emerging quantum technologies such as microelectromechanical systems (16), quantum information processing (17, 18), and circuit quantum electrodynamics, where the dynamical Casimir effect has been recently demonstrated (19, 20). Here we show that effectively one-dimensional (1D) transmission-line environments can induce strongly enhanced and longer-range van der Waals and Casimir interactions compared with free space. Such enhanced interactions may have profound implications on the quantum technologies mentioned above and give rise to a variety of new many-body phenomena involving polarizable particles in effectively 1D environments.A key point in determining how these interactions depend on distance is the spatial propagation and scattering of the virtual photon modes that mediate them. Like any other waves, photons are scattered differently off objects with different geometries. For example, light is much more effectively scattered off a mirror than off a point-like atom. This explains the stronger and longer-range vacuum interaction between mirrors (3), compared with that between atoms (2). This idea also underlies the dependence of Casimir forces on the geometrical shape of the interacting objects. Here, we take a somewhat different approach toward the geometry dependence of vdW- and Casimir-related phenomena. Instead of considering the interaction energy of extended objects with different geometries, we revisit the original Casimir and Polder (2) configuration of a pair of point-like dipoles while changing the geometry of their surrounding environment such that it confines the propagation of virtual photons to a certain direction. More specifically, we consider the energy of the interaction between two dipoles, mediated by vacuum photon modes along a 1D transmission line (TL). The resulting attractive interaction is found to be much stronger and longer range than its free-space counterpart. Surprisingly, this interaction scales with the interdipolar distance r as const. + (r/λ) ln(r/λ) or as 1/r³ for shorter or longer r than the typical dipolar wavelength λ, respectively, as opposed to the corresponding 1/r⁶ or 1/r⁷ scalings in free space (2, 4). This enhancement implies a drastic modification of Casimir-related effects for many-body and bulk polarizable systems in such an effectively 1D geometry.This article is organized as follows: Analysis Principles presents the analytical approaches used to obtain the van der Waals and Casimir interactions in a TL environment, Eqs. 6 and 7. Predictions reveals the giant enhancement of these interactions by comparing them to the case of free space (see Fig. 3 C and D), considering possible experimental realizations and imperfections. The consequences of this giant interaction to generalized Casimir effects in 1D is addressed in Prospects: Casimir Physics in 1D, followed by Conclusions.Open in a separate windowFig. 3.The TEM-mode–mediated interaction potential as a function of interdipolar distance z. (A) Log–log plot of F(z), Eq. 6. For long distances, z ≫ λ_e, the linear dependence implies a power-law behavior as in Eq. 7. (B) F(z) at short distances. (C) Log–log plot of the ratio between the TEM-mediated energy U(z), Eq. 6, and the free-space vdW energy at short distances z ≪ λ_e, U_fs(z) = ?(|d_e|⁴/48π²?²E_e)(1/z⁶) (26), with |de⊥|2=(2/3)|de|2 and A1,2=a (main text). Here a = 10⁻⁴λ_e, consistent with typical cases considered in the main text (Predictions), where a equals approximately a few micrometers and E_e/(2πℏ) equals approximately a few gigahertz. Beyond z ∼ 10⁻³λ_e, the huge enhancement of the interaction with respect to its free-space counterpart is apparent. (D) Same as C, but for long distances z ≫ λ_e, where the free-space energy takes the Casimir–Polder form, Ufs(z)=−(23/64π3)(ℏc/ϵ2)(4/9)(|de|4/Ee2)(1/z7) (26).     

Residue level quantification of protein stability in living cells

The intracellular milieu differs from the dilute conditions in which most biophysical and biochemical studies are performed. This difference has led both experimentalists and theoreticians to tackle the challenging task of understanding how the intracellular environment affects the properties of biopolymers. Despite a growing number of in-cell studies, there is a lack of quantitative, residue-level information about equilibrium thermodynamic protein stability under nonperturbing conditions. We report the use of NMR-detected hydrogen–deuterium exchange of quenched cell lysates to measure individual opening free energies of the 56-aa B1 domain of protein G (GB1) in living Escherichia coli cells without adding destabilizing cosolutes or heat. Comparisons to dilute solution data (pH 7.6 and 37 °C) show that opening free energies increase by as much as 1.14 ± 0.05 kcal/mol in cells. Importantly, we also show that homogeneous protein crowders destabilize GB1, highlighting the challenge of recreating the cellular interior. We discuss our findings in terms of hard-core excluded volume effects, charge–charge GB1-crowder interactions, and other factors. The quenched lysate method identifies the residues most important for folding GB1 in cells, and should prove useful for quantifying the stability of other globular proteins in cells to gain a more complete understanding of the effects of the intracellular environment on protein chemistry.Proteins function in a heterogeneous and crowded intracellular environment. Macromolecules comprise 20–30% of the volume of an Escherichia coli cell and reach concentrations of 300–400 g/L (1, 2). Theory predicts that the properties of proteins and nucleic acids can be significantly altered in cells compared with buffer alone (3, 4). Nevertheless, most biochemical and biophysical studies are conducted under dilute (<10 g/L macromolecules) conditions. Here, we augment the small but growing list of reports probing the equilibrium thermodynamic stability of proteins in living cells (5–9), and provide, to our knowledge, the first measurement of residue-level stability under nonperturbing conditions.Until recently, the effects of macromolecular crowding on protein stability were thought to be caused solely by hard-core, steric repulsions arising from the impenetrability of matter (4, 10, 11). The expectation was that crowding enhances stability by favoring the compact native state over the ensemble of denatured states. Increased attention to transient, nonspecific protein-protein interactions (12–15) has led both experimentalists (16–19) and theoreticians (20–22) to recognize the effects of chemical interactions between crowder and test protein when assessing the net effect of macromolecular crowding. These weak, nonspecific interactions can reinforce or oppose the effect of hard-core repulsions, resulting in increased or decreased stability depending on the chemical nature of the test protein and crowder (23–26).We chose the B1 domain of streptococcal protein G (GB1) (27) as our test protein because its structure, stability and folding kinetics have been extensively studied in dilute solution (28–38). Its small size (56 aa; 6.2 kDa) and high thermal stability make GB1 well suited for studies by NMR spectroscopy.Quantifying the equilibrium thermodynamic stability of proteins relies on determining the relative populations of native and denatured states. Because the denatured state ensemble of a stable protein is sparsely populated under native conditions, stability is usually probed by adding heat or a cosolute to promote unfolding so that the concentration ratio of the two states can be determined (39). However, stability can be measured without these perturbations by exploiting the phenomenon of backbone amide H/D exchange (40) detected by NMR spectroscopy (41). The observed rate of amide proton (N–H) exchange, k_obs, is related to equilibrium stability by considering a protein in which each N–H exists in an open (exposed, exchange-competent) state, or a closed (protected, exchange-incompetent) state (40, 42):closed(N−H)⇌kclkopopen(N−H)→kintopen(N−D)⇌kopkclclosed(N−D).[1]Each position opens and closes with rate constants, k_op and k_cl (where K_op = k_op/k_cl), and exchange from the open state occurs with intrinsic rate constant, k_int. Values for k_int are based on exchange data from unstructured peptides (43, 44). If the test protein is stable (i.e., k_cl >> k_op), the observed rate becomes:kobs=kopkintkcl+kint.[2]Exchange occurs within two limits (42). At the EX1 limit, closing is rate determining, and k_obs = k_op. This limit is usually observed for less stable proteins and at basic pH (45). Most globular proteins undergo EX2 kinetics, where exchange from the open state is rate limiting (i.e., k_cl >> k_int), and k_obs values can be converted to equilibrium opening free energies, ΔGop°′ (46):kobs=kopkclkint=Kopkint[3]ΔGop°′=−RT⁡lnkobskint,[4]where RT is the molar gas constant multiplied by the absolute temperature.The backbone amides most strongly involved in H-bonded regions of secondary structure exchange only from the fully unfolded state, yielding a maximum value of ΔGop°′ (47–49). For these residues ΔGop°′ approximates the free energy of denaturation, ΔGden°′, providing information on global stability. Lower amplitude fluctuations of the native state can give rise to partially unfolded forms (50), resulting in residues with ΔGop°′ values less than those of the global unfolders.In summary, NMR-detected H/D exchange can measure equilibrium thermodynamic stability of a protein at the level of individual amino acid residues under nonperturbing conditions. Inomata et al. (51) used this technique to measure k_obs values in human cells for four residues in ubiquitin, but experiments confirming the exchange mechanism were not reported and opening free energies were not quantified. Our results fill this void and provide quantitative residue-level protein stability measurements in living cells under nonperturbing conditions.     

Metastability and discrete spectrum of long-range systems

Long-lived quasi-stationary states (QSSs) are a signature characteristic of long-range interacting systems both in the classical and in the quantum realms. Often, they emerge after a sudden quench of the Hamiltonian internal parameters and present a macroscopic lifetime, which increases with the system size. Despite their ubiquity, the fundamental mechanism at their root remains unknown. Here, we show that the spectrum of systems with power-law decaying couplings remains discrete up to the thermodynamic limit. As a consequence, several traditional results on the chaotic nature of the spectrum in many-body quantum systems are not satisfied in the presence of long-range interactions. In particular, the existence of QSSs may be traced back to the finiteness of Poincaré recurrence times. This picture justifies and extends known results on the anomalous magnetization dynamics in the quantum Ising model with power-law decaying couplings. The comparison between the discrete spectrum of long-range systems and more conventional examples of pure point spectra in the disordered case is also discussed.

Equilibration is at the roots of thermodynamics and has been verified under general conditions in a wide range of physical systems. The current scientific literature has focused on several aspects of this problem, starting from quantum quenches and relaxation (1, 2) and arriving at thermalization of integrable and quasi-integrable systems (3–5), typicality as a foundation of quantum statistical mechanics (6–8) and many others.Despite the ubiquity of equilibration, or possibly due to it, the known examples of diverging equilibration times and recurrent behavior have attracted wide attention in modern physics. Dynamical protocols, where the system initially relaxes into a long-lived state and then undergoes actual equilibration on a longer timescale, are commonly referred to as metastable. The observation of various dynamical regimes, separated by distinct timescales, is the most common evidence of metastability and is found in several classical systems and, especially, glasses (9–11). In closed quantum systems ordinary examples of metastability appear in the presence of localized states (2, 12, 13), whose energy eigenvalues are separated from the rest of the spectrum. An analogous spectral structure justifies the observation of metastability also in open quantum systems (14).Diverging equilibration times in the thermodynamic limit are also a notorious characteristic of long-range interacting systems. A physical system is said to be long range when the two-body interaction potential decays as a power law of the distance r between its microscopic components: V(r)∼r−α in the large distance (r→∞) limit. If one focuses on the thermodynamic behavior, two main regimes appear as a function of α. For α>d, where d is the spatial dimension of the system, textbook thermodynamics is well defined and long-range interactions alter the universal scaling only close to critical points (15). We refer to this regime (α>d) as weak long-range interactions.Conversely, for α<d the thermodynamic quantities become nonadditive, leading to apparently paradoxical predictions such as ensemble inequivalence or negative specific heat and susceptibilities (16). In the out-of-equilibrium realm, the most striking property of strong long-range systems is the appearance of quasi-stationary states (QSSs), i.e., metastable configurations whose lifetime scales superlinearly with the system size. QSSs have been mainly studied in classical systems, such as the Hamiltonian mean-field model (17), where an ensemble of plane rotators is subject to a fully connected flat interaction (α=0). There, QSSs are often described in terms of the magnetization dynamics, which, after a sudden quench from an appropriate set of initial conditions, stabilize to a different value with respect to their equilibrium expectation. Then, actual equilibration occurs only after a macroscopic timescale τ∝Nβ with β>0 (16). Apart from this peculiar case, QSSs are characteristic of long-range interactions (18), ranging from gravitational (19) to electromagnetic systems (20).The progress in experiments with atomic molecular and optical systems has largely broadened the interest in long-range physics, due to the possibility of realizing nonlocal interactions via several different means, such as dipolar systems (21–23), cold atoms excited into Rydberg states (24), and trapped ions (25). In the context of metastable dynamics and QSSs a crucial role is played by cold atoms confined in optical resonators, where the photons are stored within the cavity for a sufficiently long time and mediate interactions whose range extends over the entire cavity volume (26). At the semiclassical level, a strict relation between the dynamics of cold atoms into cavity systems and the one of the Hamiltonian mean-field model has been demonstrated (27), designating these devices as optimal candidates for the observation of slow or absent equilibration.Given this broad physical interest, as well as the universal presence of QSSs in long-range interacting systems, it is surprising that the general mechanism at the root of their existence has still to be identified. Indeed, while most results concerning QSSs in classical systems derive from numerical simulations (16), first evidences of their appearance in the quantum realm have been rooted in an analytic approach, which was, however, restricted to a 1/2-spin Hamiltonian with specific boundaries of the quench protocol (28).In this paper, we will prove that the absence of equilibration of long-range quantum systems is directly connected to the persistence of finite Poincaré recurrence times also in the thermodynamic limit. Hence, the physics of macroscopic long-range systems cannot be described by the “traditional” thermodynamic limit procedure. This is in agreement with well-known observations of properties, which are common to thermodynamically large long-range systems and finite local ones, such as the impossibility to fully disregard boundary over bulk phenomena (29, 30), the existence of concave entropy regions (31), or the presence of a macroscopic energy gap between the ground state and the first excited state (32, 33).All of the above features are consequences of the spectral properties of long-range many-body systems, whose spectrum does not become continuous in the thermodynamic limit. Indeed, the eigenvalues of a long-range coupling matrix can be shown to remain discrete even in the infinite components limit, forming a pure point spectrum (34) similar to the one observed in celebrated examples of disordered systems (35). However, at variance with most disordered systems, the spectrum of strong long-range interactions possesses no continuous subspace in the thermodynamic limit, in analogy with the case of the Anderson model at infinite disorder strength (36–38).This paper is organized as follows: In H Theorem and Kinematical Chaos we outline the general picture for equilibration in closed integrable quantum systems. In Spectrum of Long-Range Systems a proof of the spectral discreteness of long-range couplings in the thermodynamic limit is presented in the case of the tight-binding chain. Then, in Vanishing Recurrence Time in the N → ∞ Limit, the connection between this result and the vanishing of the Poincaré recurrence times for critical quenches in a generic quantum system is explored. In QSSs in Spin Systems, the above picture is employed to justify the observation of diverging equilibration times in a long-range Ising model, quenched across its quantum critical point (28). In Lack of Equilibration and Relation with Disorder lack of equilibration is shown in an ensemble of long-range coupled spin waves for a generic (noncritical) quench. Finally, in Discussion the conclusive remarks are reported.     

Dynamic rupture initiation and propagation in a fluid-injection laboratory setup with diagnostics across multiple temporal scales

Fluids are known to trigger a broad range of slip events, from slow, creeping transients to dynamic earthquake ruptures. Yet, the detailed mechanics underlying these processes and the conditions leading to different rupture behaviors are not well understood. Here, we use a laboratory earthquake setup, capable of injecting pressurized fluids, to compare the rupture behavior for different rates of fluid injection, slow (megapascals per hour) versus fast (megapascals per second). We find that for the fast injection rates, dynamic ruptures are triggered at lower pressure levels and over spatial scales much smaller than the quasistatic theoretical estimates of nucleation sizes, suggesting that such fast injection rates constitute dynamic loading. In contrast, the relatively slow injection rates result in gradual nucleation processes, with the fluid spreading along the interface and causing stress changes consistent with gradually accelerating slow slip. The resulting dynamic ruptures propagating over wetted interfaces exhibit dynamic stress drops almost twice as large as those over the dry interfaces. These results suggest the need to take into account the rate of the pore-pressure increase when considering nucleation processes and motivate further investigation on how friction properties depend on the presence of fluids.

The close connection between fluids and faulting has been revealed by a large number of observations, both in tectonic settings and during human activities, such as wastewater disposal associated with oil and gas extraction, geothermal energy production, and CO₂ sequestration (1–11). On and around tectonic faults, fluids also naturally exist and are added at depths due to rock-dehydration reactions (12–15) Fluid-induced slip behavior can range from earthquakes to slow, creeping motion. It has long been thought that creeping and seismogenic fault zones have little to no spatial overlap. Nonetheless, growing evidence suggests that the same fault areas can exhibit both slow and dynamic slip (16–19). The existence of large-scale slow slip in potentially seismogenic areas has been revealed by the presence of transient slow-slip events in subduction zones (16, 18) and proposed by studies investigating the physics of foreshocks (20–22).Numerical and laboratory modeling has shown that such complex fault behavior can result from the interaction of fluid-related effects with the rate-and-state frictional properties (9, 14, 19, 23, 24); other proposed rheological explanations for complexities in fault stability include combinations of brittle and viscous rheology (25) and friction-to-flow transitions (26). The interaction of frictional sliding and fluids results in a number of coupled and competing mechanisms. The fault shear resistance τres is typically described by a friction model that linearly relates it to the effective normal stress σ^n via a friction coefficient f:τres=f σ^n=f (σn−p),[1]where σn is the normal stress acting across the fault and p is the pore pressure. Clearly, increasing pore pressure p would reduce the fault frictional resistance, promoting the insurgence of slip. However, such slip need not be fast enough to radiate seismic waves, as would be characteristic of an earthquake, but can be slow and aseismic. In fact, the critical spatial scale h* for the slipping zone to reach in order to initiate an unstable, dynamic event is inversely proportional to the effective normal stress (27, 28) and hence increases with increasing pore pressure, promoting stable slip. This stabilizing effect of increasing fluid pressure holds for both linear slip-weakening and rate-and-state friction; it occurs because lower effective normal stress results in lower fault weakening during slip for the same friction properties. For example, the general form for two-dimensional (2D) theoretical estimates of this so-called nucleation size, h*, on rate-and-state faults with steady-state, velocity-weakening friction is given by:h*=(μ*DRS)/[F(a,b)(σn−p)],[2]where μ*=μ/(1−ν) for modes I and II, and μ*=μ for mode III (29); DRS is the characteristic slip distance; and F(a, b) is a function of the rate-and-state friction parameters a and b. The function F(a, b) depends on the specific assumptions made to obtain the estimate: FRR(a,b)=4(b−a)/π (ref. 27, equation 40) for a linearized stability analysis of steady sliding, or FRA(a,b)=[π(b−a)2]/2b, with a/b>1/2 for quasistatic crack-like expansion of the nucleation zone (ref. 30, equation 42).Hence, an increase in pore pressure induces a reduction in the effective normal stress, which both promotes slip due to lower frictional resistance and increases the critical length scale h*, potentially resulting in slow, stable fault slip instead of fast, dynamic rupture. Indeed, recent field and laboratory observations suggest that fluid injection triggers slow slip first (4, 9, 11, 31). Numerical modeling based on these effects, either by themselves or with an additional stabilizing effect of shear-layer dilatancy and the associated drop in fluid pressure, have been successful in capturing a number of properties of slow-slip events observed on natural faults and in field fluid-injection experiments (14, 24, 32–34). However, understanding the dependence of the fault response on the specifics of pore-pressure increase remains elusive. Several studies suggest that the nucleation size can depend on the loading rate (35–38), which would imply that the nucleation size should also depend on the rate of friction strength change and hence on the rate of change of the pore fluid pressure. The dependence of the nucleation size on evolving pore fluid pressure has also been theoretically investigated (39). However, the commonly used estimates of the nucleation size (Eq. 2) have been developed for faults under spatially and temporally uniform effective stress, which is clearly not the case for fluid-injection scenarios. In addition, the friction properties themselves may change in the presence of fluids (40–42). The interaction between shear and fluid effects can be further affected by fault-gauge dilation/compaction (40, 43–45) and thermal pressurization of pore fluids (42, 46–48).Recent laboratory investigations have been quite instrumental in uncovering the fundamentals of the fluid-faulting interactions (31, 45, 49–57). Several studies have indicated that fluid-pressurization rate, rather than injection volume, controls slip, slip rate, and stress drop (31, 49, 57). Rapid fluid injection may produce pressure heterogeneities, influencing the onset of slip. The degree of heterogeneity depends on the balance between the hydraulic diffusion rate and the fluid-injection rate, with higher injection rates promoting the transition from drained to locally undrained conditions (31). Fluid pressurization can also interact with friction properties and produce dynamic slip along rate-strengthening faults (50, 51).In this study, we investigate the relation between the rate of pressure increase on the fault and spontaneous rupture nucleation due to fluid injection by laboratory experiments in a setup that builds on and significantly develops the previous generations of laboratory earthquake setup of Rosakis and coworkers (58, 59). The previous versions of the setup have been used to study key features of dynamic ruptures, including sub-Rayleigh to supershear transition (60); rupture directionality and limiting speeds due to bimaterial effects (61); pulse-like versus crack-like behavior (62); opening of thrust faults (63); and friction evolution (64). A recent innovation in the diagnostics, featuring ultrahigh-speed photography in conjunction with digital image correlation (DIC) (65), has enabled the quantification of the full-field behavior of dynamic ruptures (66–68), as well as the characterization of the local evolution of dynamic friction (64, 69). In these prior studies, earthquake ruptures were triggered by the local pressure release due to an electrical discharge. This nucleation procedure produced only dynamic ruptures, due to the nearly instantaneous normal stress reduction.To study fault slip triggered by fluid injection, we have developed a laboratory setup featuring a hydraulic circuit capable of injecting pressurized fluid onto the fault plane of a specimen and a set of experimental diagnostics that enables us to detect both slow and fast fault slip and stress changes. The range of fluid-pressure time histories produced by this setup results in both quasistatic and dynamic rupture nucleation; the diagnostics allows us to capture the nucleation processes, as well as the resulting dynamic rupture propagation. In particular, here, we explore two injection techniques: procedure 1, a gradual, and procedure 2, a sharp fluid-pressure ramp-up. An array of strain gauges, placed on the specimen’s surface along the fault, can capture the strain (translated into stress) time histories over a wide range of temporal scales, spanning from microseconds to tens of minutes. Once dynamic ruptures nucleate, an ultrahigh-speed camera records images of the propagating ruptures, which are turned into maps of full-field displacements, velocities, and stresses by a tailored DIC) analysis. One advantage of using a specimen made of an analog material, such as poly(methyl meth-acrylate) (PMMA) used in this study, is its transparency, which allows us to look at the interface through the bulk and observe fluid diffusion over the interface. Another important advantage of using PMMA is that its much lower shear modulus results in much smaller nucleation sizes h* than those for rocks, allowing the experiments to produce both slow and fast slip in samples of manageable sizes.We start by describing the laboratory setup and the diagnostics monitoring the pressure evolution and the slip behavior. We then present and discuss the different slip responses measured as a result of slow versus fast fluid injection and interpret our measurements by using the rate-and-state friction framework and a pressure-diffusion model.     

Low-Reynolds-number,biflagellated Quincke swimmers with multiple forms of motion

In the limit of zero Reynolds number (Re), swimmers propel themselves exploiting a series of nonreciprocal body motions. For an artificial swimmer, a proper selection of the power source is required to drive its motion, in cooperation with its geometric and mechanical properties. Although various external fields (magnetic, acoustic, optical, etc.) have been introduced, electric fields are rarely utilized to actuate such swimmers experimentally in unbounded space. Here we use uniform and static electric fields to demonstrate locomotion of a biflagellated sphere at low Re via Quincke rotation. These Quincke swimmers exhibit three different forms of motion, including a self-oscillatory state due to elastohydrodynamic–electrohydrodynamic interactions. Each form of motion follows a distinct trajectory in space. Our experiments and numerical results demonstrate a method to generate, and potentially control, the locomotion of artificial flagellated swimmers.

In a Newtonian fluid, locomotion of microswimmers requires nonreciprocal body motions (1–3). Bacteria or eukaryotic cells achieve this by beating or rotating their slender hair-like organelles, flagella (4, 5) or cilia (6), powered by molecular motors. Mimicking these organisms, artificial swimmers propelled by rotating helices (7, 8) or whipping filaments (9–12) have been fabricated. They are commonly driven by an external power source such as a magnetic field (7–9, 13, 14), sound (15), light (16, 17), and biological materials (12). However, there are very few electrically powered microswimmers (18–20), although electric fields have been exploited to drive other active systems (21–26) via a phenomenon called Quincke rotation (27).Quincke rotation originates from an electrohydrodynamic instability (28–30). Submerged in a liquid with permittivity εl and conductivity σl, a spherical particle with permittivity εs and electric conductivity σs is polarized under a uniform, steady electric field E→. When the particle is stationary, the induced dipole p→ due to the free charges is parallel or antiparallel to E→ (Fig. 1A): if the particle’s relaxation time τs=εs/σs is shorter than that of the ambient liquid, τl=εl/σl, p→ points in the same direction as E→; when τs>τl, p→ is opposite to E→, which generates an electric torque Γ→Q=p→×E→ that amplifies any angular perturbation. However, due to the resisting viscous torque Γ→μ, the system becomes unstable only when E=|E→| exceeds a threshold Ec. This instability causes the particle to rotate with a constant angular velocity ω:ω=1τEEc2−1,[1]where τ=εs+2εlσs+2σl is the relaxation time of the system (see SI Appendix, SI Text, or refs. 28, 29, 31 for derivation), and the rotational axis can be in any direction perpendicular to E→. During steady-state Quincke rotation, there is a constant angle between p→ and E→ (Fig. 1A), which results in a nonzero Γ→Q.Open in a separate windowFig. 1.Quincke rotation and the experimental setup. (A) Distribution of free charge and the corresponding dipole p→ on a sphere in a uniform, steady electric field E→. The sphere is (Left) stationary, (Middle) stationary, and (Right) rotating with a constant angular velocity ω. (B) A sketch of the biflagellated swimmer. Dashed lines show the roll axis (blue) and pitch axis (green). (C) A schematic illustration of the experimental setup.Recently, a flagellated swimmer in unbounded space driven by Quincke rotation has been proposed theoretically (32, 33). In light of the theory, we built a laboratory prototype, a biflagellated Quincke swimmer composed of a spherical particle and two attached elastic filaments, as shown in Fig. 1B, and systematically studied its behaviors at low Reynolds number (Re<0.3; Materials and Methods). Varying the electric field E→ and the angle between the two filaments, the Quincke swimmers exhibit three distinct forms of motion—two unidirectional rotations, which we call roll and pitch, and a self-oscillatory rotation, due to the balances between the electrical, elastic, and hydrodynamic torques, resulting in distinct trajectories in space. Surprisingly, it was recently reported (34) that spherical bacteria Magnetococcus marinus exhibit a similar pitch motion as our biflagellated artificial swimmers, which is rarely adopted by other microorganisms. Moreover, we found a threshold tail angle that separates the swimmers’ preferred forms of rotation, and within a small range close to this threshold angle, the three forms of motion coexist.     

Label-free probe of HIV-1 TAT peptide binding to mimetic membranes

The transacting activator of transduction (TAT) protein plays a key role in the progression of AIDS. Studies have shown that a +8 charged sequence of amino acids in the protein, called the TAT peptide, enables the TAT protein to penetrate cell membranes. To probe mechanisms of binding and translocation of the TAT peptide into the cell, investigators have used phospholipid liposomes as cell membrane mimics. We have used the method of surface potential sensitive second harmonic generation (SHG), which is a label-free and interface-selective method, to study the binding of TAT to anionic 1-palmitoyl-2-oleoyl-sn-glycero-3-phospho-1′-rac-glycerol (POPG) and neutral 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) liposomes. It is the SHG sensitivity to the electrostatic field generated by a charged interface that enabled us to obtain the interfacial electrostatic potential. SHG together with the Poisson–Boltzmann equation yielded the dependence of the surface potential on the density of adsorbed TAT. We obtained the dissociation constants K_d for TAT binding to POPC and POPG liposomes and the maximum number of TATs that can bind to a given liposome surface. For POPC K_d was found to be 7.5 ± 2 μM, and for POPG K_d was 29.0 ± 4.0 μM. As TAT was added to the liposome solution the POPC surface potential changed from 0 mV to +37 mV, and for POPG it changed from −57 mV to −37 mV. A numerical calculation of K_d, which included all terms obtained from application of the Poisson–Boltzmann equation to the TAT liposome SHG data, was shown to be in good agreement with an approximated solution.The HIV type 1 (HIV-1) transacting activator of transduction (TAT) is an important regulatory protein for viral gene expression (1–3). It has been established that the TAT protein has a key role in the progression of AIDS and is a potential target for anti-HIV vaccines (4). For the TAT protein to carry out its biological functions, it needs to be readily imported into the cell. Studies on the cellular internalization of TAT have led to the discovery of the TAT peptide, a highly cationic 11-aa region (protein transduction domain) of the 86-aa full-length protein that is responsible for the TAT protein translocating across phospholipid membranes (5–8). The TAT peptide is a member of a class of peptides called cell-penetrating peptides (CPPs) that have generated great interest for drug delivery applications (ref. 9 and references therein). The exact mechanism by which the TAT peptide enters cells is not fully understood, but it is likely to involve a combination of energy-independent penetration and endocytosis pathways (8, 10). The first step in the process is high-affinity binding of the peptide to phospholipids and other components on the cell surface such as proteins and glycosaminoglycans (1, 9).The binding of the TAT peptide to liposomes has been investigated using a variety of techniques, each of which has its own advantages and limitations. Among the techniques are isothermal titration calorimetry (9, 11), fluorescence spectroscopy (12, 13), FRET (12, 14), single-molecule fluorescence microscopy (15, 16), and solid-state NMR (17). Second harmonic generation (SHG), as an interface-selective technique (18–24), does not require a label, and because SHG is sensitive to the interface potential, it is an attractive method to selectively probe the binding of the highly charged (+8) TAT peptide to liposome surfaces. Although coherent SHG is forbidden in centrosymmetric and isotropic bulk media for reasons of symmetry, it can be generated by a centrosymmetric structure, e.g., a sphere, provided that the object is centrosymmetric over roughly the length scale of the optical coherence, which is a function of the particle size, the wavelength of the incident light, and the refractive indexes at ω and 2ω (25–30). As a second-order nonlinear optical technique SHG has symmetry restrictions such that coherent SHG is not generated by the randomly oriented molecules in the bulk liquid, but can be generated coherently by the much smaller population of oriented interfacial species bound to a particle or planar surfaces. As a consequence the SHG signal from the interface is not overwhelmed by SHG from the much larger populations in the bulk media (25–28).The total second harmonic electric field, E_2ω, originating from a charged interface in contact with water can be expressed as (31–33)E2ω∝∑iχc,i(2)EωEω+∑jχinc,j(2)EωEω+χH2O(3)EωEωΦ,[1]where χc,i(2) represents the second-order susceptibility of the species i present at the interface; χinc,j(2) represents the incoherent contribution of the second-order susceptibility, arising from density and orientational fluctuations of the species j present in solution, often referred to as hyper-Rayleigh scattering; χH2O(3) is the third-order susceptibility originating chiefly from the polarization of the bulk water molecules polarized by the charged interface; Φ is the potential at the interface that is created by the surface charge; and E_ω is the electric field of the incident light at the fundamental frequency ω. The second-order susceptibility, χc,i(2), can be written as the product of the number of molecules, N, at the surface and the orientational ensemble average of the hyperpolarizability α_i⁽²⁾ of surface species i, yielding χc,i(2)=N〈αi(2)〉 (18). The bracket ?? indicates an orientational average over the interfacial molecules. The third term in Eq. 1 depicts a third-order process by which a second harmonic field is generated by a charged interface. This term is the focus of our work. The SHG signal is dependent on the surface potential created by the electrostatic field of the surface charges, often called the χ⁽³⁾ contribution to the SHG signal. The χ⁽³⁾ method has been used to extract the surface charge density of charged planar surfaces and microparticle surfaces, e.g., liposomes, polymer beads, and oil droplets in water (21, 25, 34–39).In this work, the χ⁽³⁾ SHG method is used to explore a biomedically relevant process. The binding of the highly cationic HIV-1 TAT peptide to liposome membranes changes the surface potential, thereby enabling the use of the χ⁽³⁾ method to study the binding process in a label-free manner. Two kinds of liposomes, neutral 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) and anionic 1-palmitoyl-2-oleoyl-sn-glycero-3-phospho-1′-rac-glycerol (POPG), were investigated. The chemical structures of TAT, POPC, and POPG lipids are shown in Scheme 1.Open in a separate windowScheme 1.Chemical structures of HIV-1 TAT (47–57) peptide and the POPC and POPG lipids.     

The ferroelectric photo ground state of SrTiO3: Cavity materials engineering

Optical cavities confine light on a small region in space, which can result in a strong coupling of light with materials inside the cavity. This gives rise to new states where quantum fluctuations of light and matter can alter the properties of the material altogether. Here we demonstrate, based on first-principles calculations, that such light–matter coupling induces a change of the collective phase from quantum paraelectric to ferroelectric in the SrTiO3 ground state, which has thus far only been achieved in out-of-equilibrium strongly excited conditions [X. Li et al., Science 364, 1079–1082 (2019) and T. F. Nova, A. S. Disa, M. Fechner, A. Cavalleri, Science 364, 1075–1079 (2019)]. This is a light–matter hybrid ground state which can only exist because of the coupling to the vacuum fluctuations of light, a photo ground state. The phase transition is accompanied by changes in the crystal structure, showing that fundamental ground state properties of materials can be controlled via strong light–matter coupling. Such a control of quantum states enables the tailoring of materials properties or even the design of novel materials purely by exposing them to confined light.

Engineering an out-of-equilibrium state of a material by means of strong light fields can drastically change its properties and even induce new phases altogether. This is considered a new paradigm of material design, especially when the collective behavior of particles in quantum materials can be controlled to provide novel functionalities (1, 2). Alternatively to the intense lasers necessary to reach such out-of-equilibrium states, one can achieve strong light–matter coupling by placing the material inside an optical cavity (3–11). A main advantage of this approach is that strong interaction can be achieved at equilibrium, opening up new possibilities for materials manipulation. Among the proposed effects are novel exciton insulator states (12), control of excitonic energy ordering (13), enhanced electron–phonon coupling (14), photon-mediated electron pairing (15–18), enhanced ferroelectricity (19), and multi-quasi-particles hybridization (20). One enticing possibility is, however, to change the ground state of a material and to create a new phase not through excited quasi-particles but truly as the equilibrium state.Here we show that this can be achieved in the paraelectric SrTiO3 as a photo-correlated ferroelectric ground state. This ground state, which we refer to as photo ground state, is the result of the strong coupling between matter and quantum vacuum fluctuations of light. While similar materials of the perovskite family undergo a para- to ferroelectric phase transition at low temperatures, SrTiO3 remains paraelectric (21), because the nuclear quantum fluctuations prevent the emergence of a collective polarization that is characteristic of the ferroelectric phase (22, 23). Alterations to the material that overcome a relatively small activation energy, however, can induce ferroelectricity: for instance, through isotope substitution (24), strain (25, 26), and, most notably, nonlinear excitation of the lattice by strong and resonant terahertz laser pumping (27, 28). In the latter type of experiments, a transient broken symmetry of the structure as well as macroscopic polarization indicative of a transient ferroelectric phase have been observed.By using atomistic calculations, we show that the off-resonant dressing of the lattice of SrTiO3 with the vacuum fluctuations of the photons in a cavity can suppress the nuclear quantum fluctuations in a process that is analogous to the one of dynamical localization (29): As explained in Results and Discussion, the interaction with cavity photons effectively results in an enhancement of the effective mass of the ions, thus slowing them down and reducing the importance of their quantum fluctuations. We further demonstrate that the effect of cavity-induced localization extends to finite temperatures, even when thermal lattice fluctuations overcome the quantum ones. We thus introduce a revisited paraelectric to ferroelectric phase diagram, with the cavity coupling strength as a new dimension.