Glasses denser than the supercooled liquid

When aged below the glass transition temperature, Tg, the density of a glass cannot exceed that of the metastable supercooled liquid (SCL) state, unless crystals are nucleated. The only exception is when another polyamorphic SCL state exists, with a density higher than that of the ordinary SCL. Experimentally, such polyamorphic states and their corresponding liquid–liquid phase transitions have only been observed in network-forming systems or those with polymorphic crystalline states. In otherwise simple liquids, such phase transitions have not been observed, either in aged or vapor-deposited stable glasses, even near the Kauzmann temperature. Here, we report that the density of thin vapor-deposited films of N,N′-bis(3-methylphenyl)-N,N′-diphenylbenzidine (TPD) can exceed their corresponding SCL density by as much as 3.5% and can even exceed the crystal density under certain deposition conditions. We identify a previously unidentified high-density supercooled liquid (HD-SCL) phase with a liquid–liquid phase transition temperature (TLL) ∼35 K below the nominal glass transition temperature of the ordinary SCL. The HD-SCL state is observed in glasses deposited in the thickness range of 25 to 55 nm, where thin films of the ordinary SCL have exceptionally enhanced surface mobility with large mobility gradients. The enhanced mobility enables vapor-deposited thin films to overcome kinetic barriers for relaxation and access the HD-SCL state. The HD-SCL state is only thermodynamically favored in thin films and transforms rapidly to the ordinary SCL when the vapor deposition is continued to form films with thicknesses more than 60 nm.

Glasses are formed when the structural relaxations in supercooled liquids (SCLs) become too slow, causing the system to fall out of equilibrium at the glass transition temperature (Tg). The resulting out-of-equilibrium glass state has a thermodynamic driving force to evolve toward the SCL state through physical aging (1). At temperatures just below Tg, the extent of equilibration is limited by the corresponding SCL state, while at much lower temperatures, equilibration is limited by the kinetic barriers for relaxation. As such, the degree of thermodynamic stability achieved through physical aging is limited (2).Physical vapor deposition (PVD) is an effective technique to overcome kinetic barriers for relaxation to produce thermodynamically stable glasses (3–10). The accelerated equilibration in these systems is due to their enhanced surface mobility (11–14). During PVD, when the substrate temperature is held below Tg, molecules or atoms can undergo rearrangements and adopt more stable configurations at the free surface and proximate layers underneath (13). After the molecules are buried deeper into the film, their relaxation dynamics significantly slow down, which prevents further equilibration. Through this surface-mediated equilibration process, stable glasses can achieve low-energy states on the potential energy landscape that would otherwise require thousands or millions of years of physical aging (2, 3, 15, 16).As such, the degree of enhanced surface mobility and mobility gradients are critical factors in the formation of stable glasses (3, 11, 17, 18). While the effect of film thickness on the surface mobility and gradients of liquid-quenched (LQ) glasses has been studied in the past (19, 20), there are limited data on the role of film thickness in the stability of vapor-deposited glasses. In vapor-deposited toluene, it has been shown that decreasing the film thickness from 70 to 5 nm can increase the thermodynamic stability but decrease the apparent kinetic stability (5, 6). In contrast, thin films covered with a top layer of another material do not show a significant evidence of reduced kinetic stability (21), indicating the nontrivial role of mobility gradients in thermal and kinetic stability.Stable glasses of most organic molecules, with short-range intramolecular interactions, have properties that are indicative of the same corresponding metastable SCL state as LQ and aged glasses, without any evidence of the existence of generic liquid–liquid phase transitions that can potentially provide a resolution for the Kauzmann entropy crisis (22). The Kauzmann crisis occurs at the Kauzmann temperature (TK), where the extrapolated SCL has the same structural entropy as the crystal, producing thermodynamically impossible states just below this temperature. Recently, Beasley et al. (16) showed that near-equilibrium states of ethylbenzene can be produced using PVD down to 2 K above TK and hypothesized that any phase transition to an “ideal glass” state to avoid the Kauzmann crisis must occur at TK.In some glasses of elemental substances (23, 24) and hydrogen-bonding compounds (25, 26), liquid–liquid phase transitions can occur between polyamorphic states with distinct local packing structures that correspond to polymorphic crystalline phases. For example, at high pressures, high- and low-density supercooled water phases are interconvertible through a first-order phase transition (27, 28). Recent studies have demonstrated that such polyamorphic states can also be accessed through PVD in hydrogen-bonding systems with polymorphic crystal states at depositions above the nominal Tg (29, 30). However, these structure-specific transitions do not provide a general resolution for the Kauzmann crisis.Here, we report the observation of a liquid–liquid phase transition in vapor-deposited thin films of N,N′-bis(3-methylphenyl)-N,N′-diphenylbenzidine (TPD). TPD is a molecular glass former with only short-range intermolecular interactions. When thin films of TPD are vapor deposited onto substrates held at deposition temperatures (Tdep) below the nominal glass transition temperature of bulk TPD, Tg (bulk), films in the thickness range of 25 nm<h<55 nm achieve a high-density supercooled liquid (HD-SCL) state, which has not been previously observed. The liquid–liquid phase transition temperature (TLL) between the ordinary SCL and HD-SCL states is measured to be TLL≃Tg(bulk)−35 K. The density of thin films deposited below TLL tangentially follows the HD-SCL line, which has a stronger temperature dependence than the ordinary SCL. When vapor deposition is continued to produce thicker films (h>60 nm), the HD-SCL state transforms into the ordinary SCL state, indicating that the HD-SCL is only thermodynamically favored in the thin-film geometry. This transition is qualitatively different from the previously reported liquid–liquid phase transitions, as it is not related to a specific structural motif in TPD crystals, and it can only be observed in thin films, indicating that the energy landscape of thin films is favoring this high-density state.We observe an apparent correlation between enhanced mobility gradients in LQ thin films of TPD and the thickness range where HD-SCL states are produced during PVD. We hypothesize that enhanced mobility gradients are essential in providing access to regions of the energy landscape corresponding to the HD-SCL state, which are otherwise kinetically inaccessible. This hypothesis should be further investigated to better understand the origin of this phenomenon.     

From hidden order to antiferromagnetism: Electronic structure changes in Fe-doped URu2Si2

In matter, any spontaneous symmetry breaking induces a phase transition characterized by an order parameter, such as the magnetization vector in ferromagnets, or a macroscopic many-electron wave function in superconductors. Phase transitions with unknown order parameter are rare but extremely appealing, as they may lead to novel physics. An emblematic and still unsolved example is the transition of the heavy fermion compound URu2Si2 (URS) into the so-called hidden-order (HO) phase when the temperature drops below T0=17.5 K. Here, we show that the interaction between the heavy fermion and the conduction band states near the Fermi level has a key role in the emergence of the HO phase. Using angle-resolved photoemission spectroscopy, we find that while the Fermi surfaces of the HO and of a neighboring antiferromagnetic (AFM) phase of well-defined order parameter have the same topography, they differ in the size of some, but not all, of their electron pockets. Such a nonrigid change of the electronic structure indicates that a change in the interaction strength between states near the Fermi level is a crucial ingredient for the HO to AFM phase transition.

The transition of URu2Si2 from a high-temperature paramagnetic (PM) phase to the hidden-order (HO) phase below T0 is accompanied by anomalies in specific heat (1–3), electrical resistivity (1, 3), thermal expansion (4), and magnetic susceptibility (2, 3) that are all typical of magnetic ordering. However, the small associated antiferromagnetic (AFM) moment (5) is insufficient to explain the large entropy loss and was shown to be of extrinsic origin (6). Inelastic neutron scattering (INS) experiments revealed gapped magnetic excitations below T0 at commensurate and incommensurate wave vectors (7–9), while an instability and partial gapping of the Fermi surface was observed by angle-resolved photoemission spectroscopy (ARPES) (10–16) and scanning tunneling microscopy/spectroscopy (17, 18). More recently, high-resolution, low-temperature ARPES experiments imaged the Fermi surface reconstruction across the HO transition, unveiling the nesting vectors between Fermi sheets associated with the gapped magnetic excitations seen in INS experiments (14, 19) and quantitatively explaining, from the changes in Fermi surface size and quasiparticle mass, the large entropy loss in the HO phase (19). Nonetheless, the nature of the HO parameter is still hotly debated (20–23).The HO phase is furthermore unstable above a temperature-dependent critical pressure of about 0.7 GPa at T=0, at which it undergoes a first-order transition into a large moment AFM phase where the value of the magnetic moment per U atom exhibits a sharp increase, by a factor of 10 to 50 (6, 24–30). When the system crosses the HO → AFM phase boundary, the characteristic magnetic excitations of the HO phase are either suppressed or modified (8, 31), while resistivity and specific heat measurements suggest that the partial gapping of the Fermi surface is enhanced (24, 27).As the AFM phase has a well-defined order parameter, studying the evolution of the electronic structure across the HO/AFM transition would help develop an understanding of the HO state. So far, the experimental determination of the Fermi surface by Shubnikov de Haas (SdH) oscillations only showed minor changes across the HO → AFM phase boundary (32). Here, we take advantage of the HO/AFM transition induced by chemical pressure in URu2Si2, through the partial substitution of Ru with Fe (33–37), to directly probe its electronic structure in the AFM phase using ARPES. As we shall see, our results reveal that changes in the Ru 4d–U 5f hybridization across the HO/AFM phase boundary seem essential for a better understanding of the HO state.     

Unusual magnetotransport in twisted bilayer graphene

We present transport measurements of bilayer graphene with a 1.38^∘ interlayer twist. As with other devices with twist angles substantially larger than the magic angle of 1.1^∘, we do not observe correlated insulating states or band reorganization. However, we do observe several highly unusual behaviors in magnetotransport. For a large range of densities around half filling of the moiré bands, magnetoresistance is large and quadratic. Over these same densities, the magnetoresistance minima corresponding to gaps between Landau levels split and bend as a function of density and field. We reproduce the same splitting and bending behavior in a simple tight-binding model of Hofstadter’s butterfly on a triangular lattice with anisotropic hopping terms. These features appear to be a generic class of experimental manifestations of Hofstadter’s butterfly and may provide insight into the emergent states of twisted bilayer graphene.

The mesmerizing Hofstadter butterfly spectrum arises when electrons in a two-dimensional periodic potential are immersed in an out-of-plane magnetic field. When the magnetic flux Φ through a unit cell is a rational multiple p / q of the magnetic flux quantum Φ0=h/e, each Bloch band splits into q subbands (1). The carrier densities corresponding to gaps between these subbands follow straight lines when plotted as a function of normalized density n/ns and magnetic field (2). Here, n_s is the density of carriers required to fill the (possibly degenerate) Bloch band. These lines can be described by the Diophantine equation (n/ns)=t(Φ/Φ0)+s for integers s and t. In experiments, they appear as minima or zeros in longitudinal resistivity coinciding with Hall conductivity quantized at σxy=te2/h (3, 4). Hofstadter originally studied magnetosubbands emerging from a single Bloch band on a square lattice. In the following decades, other authors considered different lattices (5–7), the effect of anisotropy (6, 8–10), next-nearest-neighbor hopping (11–15), interactions (16, 17), density wave states (9), and graphene moirés (18, 19).It took considerable ingenuity to realize clean systems with unit cells large enough to allow conventional superconducting magnets to reach Φ/Φ0∼1. The first successful observation of the butterfly in electrical transport measurements was in GaAs/AlGaAs heterostructures with lithographically defined periodic potentials (20–22). These experiments demonstrated the expected quantized Hall conductance in a few of the largest magnetosubband gaps. In 2013, three groups mapped out the full butterfly spectrum in both density and field in heterostructures based on monolayer (23, 24) and bilayer (25) graphene. In all three cases, the authors made use of the 2% lattice mismatch between their graphene and its encapsulating hexagonal boron nitride (hBN) dielectric. With these layers rotationally aligned, the resulting moiré pattern was large enough in area that gated structures studied in available high-field magnets could simultaneously approach normalized carrier densities and magnetic flux ratios of 1. Later work on hBN-aligned bilayer graphene showed that, likely because of electron–electron interactions, the gaps could also follow lines described by fractional s and t (26).In twisted bilayer graphene (TBG), a slight interlayer rotation creates a similar-scale moiré pattern. Unlike with graphene–hBN moirés, in TBG there is a gap between lowest and neighboring moiré subbands (27). As the twist angle approaches the magic angle of 1.1^∘ the isolated moiré bands become flat (28, 29), and strong correlations lead to fascinating insulating (30–37), superconducting (31–33, 35–37), and magnetic (34, 35, 38) states. The strong correlations tend to cause moiré subbands within a fourfold degenerate manifold to move relative to each other as one tunes the density, leading to Landau levels that project only toward higher magnitude of density from charge neutrality and integer filling factors (37, 39). This correlated behavior obscures the single-particle Hofstadter physics that would otherwise be present.In this work, we present measurements from a TBG device twisted to 1.38^∘. When we apply a perpendicular magnetic field, a complicated and beautiful fan diagram emerges. In a broad range of densities on either side of charge neutrality, the device displays large, quadratic magnetoresistance. Within the magnetoresistance regions, each Landau level associated with ν=±8,±12,±16,… appears to split into a pair, and these pairs follow complicated paths in field and density, very different from those predicted by the usual Diophantine equation. Phenomenology similar in all qualitative respects appears in measurements on several regions of this same device with similar twist angles and in two separate devices, one at 1.59^∘ and the other at 1.70^∘ (see SI Appendix for details).We reproduce the unusual features of the Landau levels (LLs) in a simple tight-binding model on a triangular lattice with anisotropy and a small energetic splitting between two species of fermions. At first glance, this is surprising, because that model does not represent the symmetries of the experimental moiré structure. We speculate that the unusual LL features we experimentally observe can generically emerge from spectra of Hofstadter models that include the same ingredients we added to the triangular lattice model. With further theoretical work it may be possible to use our measurements to gain insight into the underlying Hamiltonian of TBG near the magic angle.     

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.     

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.     

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.     

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.     

Direct evidence for a magnetic f-electron–mediated pairing mechanism of heavy-fermion superconductivity in CeCoIn5

To identify the microscopic mechanism of heavy-fermion Cooper pairing is an unresolved challenge in quantum matter studies; it may also relate closely to finding the pairing mechanism of high-temperature superconductivity. Magnetically mediated Cooper pairing has long been the conjectured basis of heavy-fermion superconductivity but no direct verification of this hypothesis was achievable. Here, we use a novel approach based on precision measurements of the heavy-fermion band structure using quasiparticle interference imaging to reveal quantitatively the momentum space (k-space) structure of the f-electron magnetic interactions of CeCoIn₅. Then, by solving the superconducting gap equations on the two heavy-fermion bands Ekα,β with these magnetic interactions as mediators of the Cooper pairing, we derive a series of quantitative predictions about the superconductive state. The agreement found between these diverse predictions and the measured characteristics of superconducting CeCoIn₅ then provides direct evidence that the heavy-fermion Cooper pairing is indeed mediated by f-electron magnetism.Superconductivity of heavy fermions is of abiding interest, both in its own right (1–7) and because it could exemplify the unconventional Cooper pairing mechanism of high-temperature superconductors (8–11). Heavy-fermion compounds are intermetallics containing magnetic ions in the 4f- or 5f-electronic state within each unit cell. At high temperatures, each f-electron is localized at a magnetic ion (Fig. 1A). At low temperatures, interactions between f-electron spins (red arrows Fig. 1A) lead to the formation of a narrow but the subtly curved f-electron band εkf near the chemical potential (red curve, Fig. 1B), and Kondo screening hybridizes this band with the conventional c-electron band εkc of the metal (black curve, Fig. 1B). As a result, two new heavy-fermion bands Ekα,β (Fig. 1C) appear within a few millielectron volts of the Fermi energy. Their electronic structure is controlled by the hybridization matrix element s_k for interconversion of conduction c-electrons to f-electrons and vice-versa, such thatEkα,β=εkc+εkf2±(εkc−εkf2)2+sk2.[1]The momentum structure of the narrow bands of hybridized electronic states (Eq. 1 and Fig. 1C, blue curves at left) near the Fermi surface then directly reflects the form of magnetic interactions encoded within the parent f-electron band εkf. It is these interactions that are conjectured to drive the Cooper pairing (1–5) and thus the opening up of a superconducting energy gap (Fig. 1C, yellow curves at right).Open in a separate windowFig. 1.Effects of f-electron magnetism in a heavy-fermion material. (A) The magnetic subsystem of CeCoIn₅ consists of almost localized magnetic f-electrons (red arrows) with a weak hopping matrix element yielding a very narrow band with strong magnetic interactions between the f-electron spins. (B) The heavy f-electron band is shown schematically in red and the light c-electron band in black. (C) On the left, schematic of the result of hybridizing the c- and f-electrons in B into new composite electronic states referred to as heavy fermions (blue). On the right, the opening of a superconducting energy gap is schematically shown by back-bending bands near the chemical potential. The microscopic interactions driving Cooper pairing of these states, and thus of heavy-fermion superconductivity, have not been identified unambiguously for any heavy-fermion compound.     

Modeling the instantaneous normal mode spectra of liquids as that of unstable elastic media

We study the instantaneous normal mode (INM) spectrum of a simulated soft-sphere liquid at different equilibrium temperatures T. We find that the spectrum of eigenvalues ρ(λ) has a sharp maximum near (but not at) λ=0 and decreases monotonically with |λ| on both the stable and unstable sides of the spectrum. The spectral shape strongly depends on temperature. It is rather asymmetric at low temperatures (close to the dynamical critical temperature) and becomes symmetric at high temperatures. To explain these findings we present a mean-field theory for ρ(λ), which is based on a heterogeneous elasticity model, in which the local shear moduli exhibit spatial fluctuations, including negative values. We find good agreement between the simulation data and the model calculations, done with the help of the self-consistent Born approximation (SCBA), when we take the variance of the fluctuations to be proportional to the temperature T. More importantly, we find an empirical correlation of the positions of the maxima of ρ(λ) with the low-frequency exponent of the density of the vibrational modes of the glasses obtained by quenching to T=0 from the temperature T. We discuss the present findings in connection to the liquid to glass transformation and its precursor phenomena.

The investigation of the potential energy surface (PES) V(r1(t)…rN(t)) of a liquid (made up of N particles with positions r1(t)…rN(t) at a time instant t) and the corresponding instantaneous normal modes (INMs) of the (Hessian) matrix of curvatures has been a focus of liquid and glass science since the appearance of Goldstein’s seminal article (1) on the relation between the PES and the liquid dynamics in the viscous regime above the glass transition (2–27).The PES has been shown to form a rather ragged landscape in configuration space (8, 28, 29) characterized by its stationary points. In a glass these points are minima and are called “inherent structures.” The PES is believed to contain important information on the liquid–glass transformation mechanism. For the latter a complete understanding is still missing (28, 30, 31). The existing molecular theory of the liquid–glass transformation is mode-coupling theory (MCT) (32, 33) and its mean-field Potts spin version (28, 34). MCT predicts a sharp transition at a temperature TMCT>Tg, where T_g is the temperature of structural arrest (glass transition temperature). MCT completely misses the heterogeneous activated relaxation processes (dynamical heterogeneities), which are evidently present around and below T_MCT and which are related to the unstable (negative-λ) part of the INM spectrum (28, 30).Near and above T_MCT, apparently, there occurs a fundamental change in the PES. Numerical studies of model liquids have shown that minima present below T_MCT change into saddles, which then explains the absence of activated processes above T_MCT (2–24). Very recently, it was shown that T_MCT is related to a localization–delocalization transition of the unstable INM modes (25, 26).The INM spectrum is obtained in molecular dynamic simulations by diagonalizing the Hessian matrix of the interaction potential, taken at a certain time instant t:Hijαβ(t)=∂2∂xi(α)∂xj(β)V{r1(t)…rN(t)},[1]with ri=(xi(1),xi(2),xi(3)). For large positive values of the eigenvalues λ_j (j=1…N, N being the number of particles in the system) they are related to the square of vibrational frequencies λj=ωj2, and one can consider the Hessian as the counterpart of the dynamical matrix of a solid. In this high-frequency regime one can identify the spectrum with the density of vibrational states (DOS) of the liquid viag(ω)=2 ωρ(λ(ω))=13N∑jδ(ω−ωj) .[2]For small and negative values of λ this identification is not possible. For the unstable part of the spectrum (λ<0) it has become common practice to call the imaginary number λ=iω˜ and define the corresponding DOS asg(ω˜)≡2 ω˜ρ(λ(ω˜)).[3]This function is plotted on the negative ω axis and the stable g(ω), according to [2], on the positive axis. However, the (as we shall see, very interesting) details of the spectrum ρ(λ) near λ = 0 become almost completely hidden by multiplying the spectrum with |ω|. In fact, it has been demonstrated by Sastry et al. (6) and Taraskin and Elliott (7) already 2 decades ago that the INM spectrum of liquids, if plotted as ρ(λ) and not as g(ω) according to [2] and [3], exhibits a characteristic cusp-like maximum at λ = 0. The shape of the spectrum changes strongly with temperature. This is what we find as well in our simulation and what we want to explore further in our present contribution.In the present contribution we demonstrate that the strong change of the spectrum with temperature can be rather well explained in terms of a model, in which the instantaneous harmonic spectrum of the liquid is interpreted to be that of an elastic medium, in which the local shear moduli exhibit strong spatial fluctuations, which includes a large number of negative values. Because these fluctuations are just a snapshot of thermal fluctuations, we assume that they are obeying Gaussian statistics, the variance of which is proportional to the temperature.Evidence for a characteristic change in the liquid configurations in the temperature range above T_g has been obtained in recent simulation studies of the low-frequency vibrational spectrum of glasses, which have been rapidly quenched from a certain parental temperature T*. If T* is decreased from high temperatures toward T_MCT, the low-frequency exponent of the vibrational DOS of the daughter glass (quenched from T* to T = 0) changed from Debye-like g(ω)∝ω2 to g(ω)∝ωs with s > 2. In our numerical investigation of the INM spectra we show a correlation of some details of the low-eigenvalue features of these spectra with the low-frequency properties of the daughter glasses obtained by quenching from the parental temperatures.The stochastic Helmholtz equations (Eq. 7) of an elastic model with spatially fluctuating shear moduli can be readily solved for the averaged Green’s functions by field theoretical techniques (35–37). Via a saddle point approximation with respect to the resulting effective field theory one arrives at a mean-field theory (self-consistent Born approximation [SCBA]) for the self-energy of the averaged Green’s functions. The SCBA predicts a stable spectrum below a threshold value of the variance. Restricted to this stable regime, this theory, called heterogeneous elasticity theory (HET), was rather successful in explaining several low-frequency anomalies in the vibrational spectrum of glasses, including the so-called boson peak, which is an enhancement at finite frequencies over the Debye behavior of the DOS g(ω)∝ω2 (37–41). We now explore the unstable regime of this theory and compare it to the INM spectrum of our simulated soft-sphere liquid.^*We start Results by presenting a comparison of the simulated spectra of the soft-sphere liquid with those obtained by the unstable version of HET-SCBA theory. We then concentrate on some specific features of the INM spectra, namely, the low-eigenvalue slopes and the shift of the spectral maximum from λ = 0. Both features are accounted for by HET-SCBA. In particular, we find an interesting law for the difference between the slopes of the unstable and the stable parts of the spectrum, which behaves as T−2/3, which, again, is accounted for by HET-SCBA.In the end we compare the shift of the spectral maximum with the low-frequency exponent of the DOS of the corresponding daughter glasses and find an empirical correlation. We discuss these results in connection with the saddle to minimum transformation near T_MCT.     

Submesoscale dispersion in the vicinity of the Deepwater Horizon spill

Reliable forecasts for the dispersion of oceanic contamination are important for coastal ecosystems, society, and the economy as evidenced by the Deepwater Horizon oil spill in the Gulf of Mexico in 2010 and the Fukushima nuclear plant incident in the Pacific Ocean in 2011. Accurate prediction of pollutant pathways and concentrations at the ocean surface requires understanding ocean dynamics over a broad range of spatial scales. Fundamental questions concerning the structure of the velocity field at the submesoscales (100 m to tens of kilometers, hours to days) remain unresolved due to a lack of synoptic measurements at these scales. Using high-frequency position data provided by the near-simultaneous release of hundreds of accurately tracked surface drifters, we study the structure of submesoscale surface velocity fluctuations in the Northern Gulf of Mexico. Observed two-point statistics confirm the accuracy of classic turbulence scaling laws at 200-m to 50-km scales and clearly indicate that dispersion at the submesoscales is local, driven predominantly by energetic submesoscale fluctuations. The results demonstrate the feasibility and utility of deploying large clusters of drifting instruments to provide synoptic observations of spatial variability of the ocean surface velocity field. Our findings allow quantification of the submesoscale-driven dispersion missing in current operational circulation models and satellite altimeter-derived velocity fields.The Deepwater Horizon (DwH) incident was the largest accidental oil spill into marine waters in history with some 4.4 million barrels released into the DeSoto Canyon of the northern Gulf of Mexico (GoM) from a subsurface pipe over ∼84 d in the spring and summer of 2010 (1). Primary scientific questions, with immediate practical implications, arising from such catastrophic pollutant injection events are the path, speed, and spreading rate of the pollutant patch. Accurate prediction requires knowledge of the ocean flow field at all relevant temporal and spatial scales. Whereas ocean general circulation models were widely used during and after the DwH incident (2–6), such models only capture the main mesoscale processes (spatial scale larger than 10 km) in the GoM. The main factors controlling surface dispersion in the DeSoto Canyon region remain unclear. The region lies between the mesoscale eddy-driven deep water GoM (7) and the wind-driven shelf (8) while also being subject to the buoyancy input of the Mississippi River plume during the spring and summer months (9). Images provided by the large amounts of surface oil produced in the DwH incident revealed a rich array of flow patterns (10) showing organization of surface oil not only by mesoscale straining into the loop current “Eddy Franklin,” but also by submesoscale processes. Such processes operate at spatial scales and involve physics not currently captured in operational circulation models. Submesoscale motions, where they exist, can directly influence the local transport of biogeochemical tracers (11, 12) and provide pathways for energy transfer from the wind-forced mesoscales to the dissipative microscales (13–15). Dynamics at the submesoscales have been the subject of recent research (16–20). However, the investigation of their effect on ocean transport has been predominantly modeling based (13, 21–23) and synoptic observations, at adequate spatial and temporal resolutions, are rare (24, 25). The mechanisms responsible for the establishment, maintenance, and energetics of such features in the Gulf of Mexico remain unclear.Instantaneous measurement of all representative spatiotemporal scales of the ocean state is notoriously difficult (26). As previously reviewed (27), traditional observing systems are not ideal for synoptic sampling of near-surface flows at the submesoscale. Owing to the large spacing between ground tracks (28) and along-track signal contamination from high-frequency motions (29), gridded altimeter-derived sea level anomalies only resolve the largest submesoscale motions. Long time-series ship-track current measurements attain similar, larger than 2 km, spatial resolutions, and require averaging the observations over evolving ocean states (30). Simultaneous, two-point accoustic Doppler current profiler measurements from pairs of ships (25) provide sufficient resolution to show the existence of energetic submesoscale fluctuations in the mixed layer, but do not explicitly quantify the scale-dependent transport induced by such motions at the surface. Lagrangian experiments, centered on tracking large numbers of water-following instruments, provide the most feasible means of obtaining spatially distributed, simultaneous measurements of the structure of the ocean’s surface velocity field on 100-m to 10-km length scales.Denoting a trajectory by x(a, t), where x(a, t₀) = a, the relative separation of a particle pair is given by D(t,D0)=x(a1,t)−x(a2,t)=D0+∫t0tΔv(t′,D0)dt′, where the Lagrangian velocity difference is defined by Δv(t, D₀) = v(a₁, t) − v(a₂, t). The statistical quantities of interest, both practically and theoretically, are the scale-dependent relative dispersion D²(t) = 〈D ⋅ D〉 (averaged over particle pairs) and the average longitudinal or separation velocity, Δv(r), at a given separation, r. The velocity scale is defined by the second order structure function Δv(r)=〈δv2〉, where δv(r) = (v(x + r) − v(x)) ⋅ r/∥r∥ (31, 32) where the averaging is now conditioned on the pair separation r.The applicability of classical dispersion theories (32–34) developed in the context of homogeneous, isotropic turbulence with localized spectral forcing, to ocean flows subject to the effects of rotation, stratification, and complex forcing at disparate length and time scales remains unresolved. Turbulence theories broadly predict two distinct dispersion regimes depending upon the shape of the spatial kinetic energy spectrum, E(k) ∼ k^−β, of the velocity field (35). For sufficiently steep spectra (β ≥ 3) the dispersion is expected to grow exponentially, D ∼ e^λt with a scale-independent rate. At the submesoscales (∼ 100 m–10 km), this nonlocal growth rate will then be determined by the mesoscale motions currently resolved by predictive models. For shallower spectra (1 < β < 3), however, the dispersion is local, D ∼ t^2/(3−β), and the growth rate of a pollutant patch is dominated by advective processes at the scale of the patch. Accurate prediction of dispersion in this regime requires resolution of the advecting field at smaller scales than the mesoscale.Whereas compilations of data from dye measurements broadly support local dispersion in natural flows (36), the range of scales in any particular dye experiment is limited. A number of Lagrangian observational studies have attempted to fill this gap. LaCasce and Ohlmann (37) considered 140 pairs of surface drifters on the GoM shelf over a 5-y period and found evidence of a nonlocal regime for temporally smoothed data at 1-km scales. Koszalka et al. (38) using ??(100) drifter pairs with D₀ < 2 km launched over 18 mo in the Norwegian Sea, found an exponential fit for D²(t) for a limited time (t = 0.5 − 2 d), although the observed longitudinal velocity structure function is less clearly fit by a corresponding quadratic. They concluded that a nonlocal dispersion regime could not be identified. In contrast, Lumpkin and Elipot (39) found evidence of local dispersion at 1-km scales using 15-m drogued drifters launched in the winter-time North Atlantic. It is not clear how the accuracy of the Argos positioning system (150–1,000 m) used in these studies affects the submesoscale dispersion estimates. Schroeder et al. (40), specifically targeting a coastal front using a multiscale sampling pattern, obtained results consistent with local dispersion, but the statistical significance (maximum 64 pairs) remained too low to be definitive.     

Moving Dirac nodes by chemical substitution

Dirac fermions play a central role in the study of topological phases, for they can generate a variety of exotic states, such as Weyl semimetals and topological insulators. The control and manipulation of Dirac fermions constitute a fundamental step toward the realization of novel concepts of electronic devices and quantum computation. By means of Angle-Resolved Photo-Emission Spectroscopy (ARPES) experiments and ab initio simulations, here, we show that Dirac states can be effectively tuned by doping a transition metal sulfide, BaNiS2, through Co/Ni substitution. The symmetry and chemical characteristics of this material, combined with the modification of the charge-transfer gap of BaCo1−xNixS2 across its phase diagram, lead to the formation of Dirac lines, whose position in k-space can be displaced along the Γ−M symmetry direction and their form reshaped. Not only does the doping x tailor the location and shape of the Dirac bands, but it also controls the metal-insulator transition in the same compound, making BaCo1−xNixS2 a model system to functionalize Dirac materials by varying the strength of electron correlations.

In the vast domain of topological Dirac and Weyl materials (1–9), the study of various underlying mechanisms (10–15) leading to the formation of nontrivial band structures is key to discovering new topological electronic states (16–23). A highly desirable feature of these materials is the tunability of the topological properties by an external parameter, which will make them suitable in view of technological applications, such as topological field-effect transistors (24). While a thorough control of band topology can be achieved, in principle, in optical lattices (25) and photonic crystals (26) through the wandering, merging, and reshaping of nodal points and lines in k-space (27, 28), in solid-state systems, such a control is much harder to achieve. Proposals have been made by using optical cavities (29), twisted van der Waals heterostructures (30), intercalation (31), chemical deposition (32, 33), impurities (34), and magnetic and electric applied fields (35), both static (36) and time-periodic (17, 37). Here, we prove that it is possible to move and reshape Dirac nodal lines in reciprocal space by chemical substitution. Namely, by means of Angle-Resolved Photo-Emission Spectroscopy (ARPES) experiments and ab initio simulations, we observe a sizable shift of robust massive Dirac nodes toward Γ in BaCo1−xNixS2 as a function of doping x, obtained by replacing Ni with Co. At variance with previous attempts of controlling Dirac states by doping (19, 38), in our work, we report both a reshape and a significant k-displacement of the Dirac nodes.BaCo1−xNixS2 is a prototypical transition metal system with a simple square lattice (39). In BaCo1−xNixS2 , the same doping parameter x that tunes the position of the Dirac nodes also controls the electronic phase diagram, which features a first-order metal-insulator transition (MIT) at a critical substitution level, xcr∼ 0.22 (40, 41), as shown in Fig. 1A. The Co rich side (x=0) is an insulator with columnar antiferromagnetic (AF) order and with local moments in a high-spin (S = 3/2) configuration (42). This phase can be seen as a spin density wave (SDW) made of antiferromagnetically coupled collinear spin chains. Both electron-correlation strength and charge-transfer gap ΔCT increase with decreasing x, as typically found in the late-transition metal series. The MIT at x=0.22 is of interest because it is driven by electron correlations (43) and is associated with a competition between an insulating antiferromagnetic phase and an unconventional paramagnetic semimetal (44), where the Dirac nodes are found at the Fermi level. We show that a distinctive feature of these Dirac states is their dominant d-orbital character and that the underlying band-inversion mechanism is driven by a large d−p hybridization combined with the nonsymmorphic symmetry (NSS) of the crystal (Fig. 1B). It follows that an essential role in controlling the properties of Dirac states is played by electron correlations and by the charge-transfer gap (Fig. 1C), as they have a direct impact on the hybridization strength. This results into an effective tunability of shape, energy, and wave vector of the Dirac lines in the proximity of the Fermi level. Specifically, the present ARPES study unveils Dirac bands moving from M to Γ with decreasing x. The bands are well explained quantitatively by ab initio calculations, in a hybrid density functional approximation suitable for including nonlocal correlations of screened-exchange type, which affect the hybridization between the d and p states. The same functional is able to describe the insulating SDW phase at x=0, driven by local correlations, upon increase of the optimal screened-exchange fraction. These calculations confirm that the Dirac nodes mobility in k-space stems directly from the evolution of the charge-transfer gap, i.e., the relative position between d and p on-site energies. These results clearly suggest that BaCo1−xNixS2 is a model system to tailor Dirac states and, more generally, that two archetypal features of correlated systems, such as the hybrid d−p bands and the charge-transfer gap, constitute a promising playground to engineer Dirac and topological materials using chemical substitution and other macroscopic control parameters.Open in a separate windowFig. 1.Experimental observation of Dirac states in the phase diagram of BaCo1−xNixS2. (A) Phase diagram of BaCo1−xNixS2. The transition lines between the PM, the paramagnetic insulator (PI), and the antiferromagnetic insulator (AFI) are reported. Colored circles indicate the different doping levels x studied in this work. This doping alters the d−p charge-transfer gap (ΔCT). (B) Crystal structure of BaNiS2. Blue, red, and yellow spheres represent the Ni, S, and Ba atoms, respectively. The tetragonal unit cell is indicated by black solid lines. Lattice parameters are a = 4.44 Å and c = 8.93 Å (45). (B, Upper) Projection of the unit cell in the xy plane, containing two Ni atoms. (C) Schematics of the energy levels. The hybridization of d− and p− orbitals creates the Dirac states, and the d−p charge-transfer gap fixes the position of these states in the E−k space. (D) A three-dimensional ARPES map of BaNiS2 (x=1) taken at 70-eV photon energy. The top surface shows the Fermi surface, and the sides of the cube present the band dispersion along high-symmetry directions. The linearly dispersing bands along Γ−M cross each other at the Fermi level, EF, thus creating four Dirac nodes. (E) We observe the oval-shaped section of the linearly dispersing bands on the kx−ky plane for E−EF=−100 meV. The linearly dispersing bands along the major and minor axis of the oval are also shown.     

Phase-separating RNA-binding proteins form heterogeneous distributions of clusters in subsaturated solutions

Macromolecular phase separation is thought to be one of the processes that drives the formation of membraneless biomolecular condensates in cells. The dynamics of phase separation are thought to follow the tenets of classical nucleation theory, and, therefore, subsaturated solutions should be devoid of clusters with more than a few molecules. We tested this prediction using in vitro biophysical studies to characterize subsaturated solutions of phase-separating RNA-binding proteins with intrinsically disordered prion-like domains and RNA-binding domains. Surprisingly, and in direct contradiction to expectations from classical nucleation theory, we find that subsaturated solutions are characterized by the presence of heterogeneous distributions of clusters. The distributions of cluster sizes, which are dominated by small species, shift continuously toward larger sizes as protein concentrations increase and approach the saturation concentration. As a result, many of the clusters encompass tens to hundreds of molecules, while less than 1% of the solutions are mesoscale species that are several hundred nanometers in diameter. We find that cluster formation in subsaturated solutions and phase separation in supersaturated solutions are strongly coupled via sequence-encoded interactions. We also find that cluster formation and phase separation can be decoupled using solutes as well as specific sets of mutations. Our findings, which are concordant with predictions for associative polymers, implicate an interplay between networks of sequence-specific and solubility-determining interactions that, respectively, govern cluster formation in subsaturated solutions and the saturation concentrations above which phase separation occurs.

Phase separation of RNA-binding proteins with disordered prion-like domains (PLDs) and RNA-binding domains (RBDs) is implicated in the formation and dissolution of membraneless biomolecular condensates such as RNA–protein (RNP) granules (1–9). Macroscopic phase separation is a process whereby a macromolecule in a solvent separates into a dilute, macromolecule-deficient phase that coexists with a dense, macromolecule-rich phase (10, 11). In a binary mixture, the soluble phase, comprising dispersed macromolecules that are well mixed with the solvent, becomes saturated at a concentration designated as c_sat. Above c_sat, for total macromolecular concentrations c_tot that are between the binodal and spinodal, phase separation of full-length RNA-binding proteins and PLDs is thought to follow classical nucleation theory (12–15).In classical nucleation theories, clusters representing incipient forms of the new dense phase form within dispersed phases of supersaturated solutions defined by c_tot > c_sat (16, 17). In the simplest formulation of classical nucleation theory (16–18), the free energy of forming a cluster of radius a is ΔF=−4π3a3Δμρn+4πa2γ. Here, Δµ is the difference in the chemical potential between the one-phase and two-phase regimes (see discussion in SI Appendix), which is negative in supersaturated solutions and positive in subsaturated solutions; ρ_n is the number of molecules per unit volume, and γ is the interfacial tension between dense and dilute phases. At temperature T, in a seed-free solution, the degree of supersaturation s is defined as s≡ΔμRT=ln(ctotcsat), where R is the ideal gas constant. Here, s is positive for c_tot > c_sat, and, as s increases, cluster formation becomes more favorable. Above a critical radius a*, the free energy of cluster formation can overcome the interfacial penalty, and the new dense phase grows in a thermodynamically downhill fashion. Ideas from classical nucleation theory have been applied to analyze and interpret the dynamics of phase separation in supersaturated solutions (12, 13, 15). Classical nucleation theories stand in contrast to two-step nucleation theories that predict the existence of prenucleation clusters in supersaturated solutions (19–22). These newer theories hint at the prospect of there being interesting features in subsaturated solutions, where c_tot < c_sat and s < 0.The subsaturated regime, where s is negative, corresponds to the one-phase regime. Ignoring the interfacial tension, the free energy of realizing clusters with n molecules in subsaturated solutions is: ΔF = –nΔµ. Therefore, the probability P(n) of forming a cluster of n molecules in a subsaturated solution is proportional to exp(sn). Accordingly, the relative probability P(n)/P(1) of forming clusters with n molecules will be exp(s(n – 1)). This quantity, which may be thought of as the concentration of clusters with n molecules, is negligibly small for clusters with more than a few molecules. This is true irrespective of the degree of subsaturation, s. Is this expectation from classical nucleation theories valid? We show here that subsaturated solutions feature a rich distribution of species not anticipated by classical nucleation theories. We report results from measurements of cluster size distributions in subsaturated solutions of phase-separating RNA-binding proteins from the FUS-EWSR1-TAF15 (FET) family. We find that these systems form clusters in subsaturated solutions, and that the cluster sizes follow heavy-tailed distributions. The abundant species are always small clusters. However, as total macromolecular concentration (c_tot) increases, the distributions of cluster sizes shift continuously toward larger values. We discuss these findings in the context of theories for associative polymers (9, 23–30).     

COVID-19 pandemic reveals persistent disparities in nitrogen dioxide pollution

The unequal spatial distribution of ambient nitrogen dioxide (NO2), an air pollutant related to traffic, leads to higher exposure for minority and low socioeconomic status communities. We exploit the unprecedented drop in urban activity during the COVID-19 pandemic and use high-resolution, remotely sensed NO2 observations to investigate disparities in NO2 levels across different demographic subgroups in the United States. We show that, prior to the pandemic, satellite-observed NO2 levels in the least White census tracts of the United States were nearly triple the NO2 levels in the most White tracts. During the pandemic, the largest lockdown-related NO2 reductions occurred in urban neighborhoods that have 2.0 times more non-White residents and 2.1 times more Hispanic residents than neighborhoods with the smallest reductions. NO2 reductions were likely driven by the greater density of highways and interstates in these racially and ethnically diverse areas. Although the largest reductions occurred in marginalized areas, the effect of lockdowns on racial, ethnic, and socioeconomic NO2 disparities was mixed and, for many cities, nonsignificant. For example, the least White tracts still experienced ∼1.5 times higher NO2 levels during the lockdowns than the most White tracts experienced prior to the pandemic. Future policies aimed at eliminating pollution disparities will need to look beyond reducing emissions from only passenger traffic and also consider other collocated sources of emissions such as heavy-duty vehicles.

Adverse air quality is an environmental justice issue, as it disproportionately affects marginalized and disenfranchised populations around the world (1–4). Growing evidence suggests that these populations experience more air pollution than is caused by their consumption (5–7). Within the United States, disparities in exposure are persistent, despite successful regulatory measures that have reduced pollution (8, 9). Nitrogen dioxide (NO2) is a short-lived trace gas formed shortly after fossil fuel combustion and regulated by the National Ambient Air Quality Standards under the Clean Air Act. Exposure to NO2 is associated with a range of respiratory diseases and premature mortality (10–12). NO2 is also a precursor to other pollutants such as ozone and particulate matter (13). Major sources of anthropogenic NO2, such as roadways and industrial facilities, are often located within or nearby marginalized and disenfranchised communities (14, 15), and disparities in NO2 exposure across demographic subgroups have been the focus of several recent studies (4, 8, 16–18).In early 2020, governments around the world imposed lockdowns and shelter-in-place orders in response to the spread of COVID-19. The earliest government-mandated lockdowns in the United States began in California on 19 March 2020, and many states followed suit in the following days. Changes in mobility patterns indicate that self-imposed social distancing practices were underway days to weeks before the formal announcement of lockdowns (19). Lockdowns led to sharp reductions in surface-level NO2 (20–23) and tropospheric column NO2 measured from satellite instruments (21, 24–27) over the United States, China, and Europe. According to government-reported inventories, roughly 60% of anthropogenic emissions of nitrogen oxides (NOx≡ NO + NO2) in the United States in 2010 were emitted by on-road vehicles (28), and up to 80% of ambient NO2 in urban areas can be linked to traffic emissions (29, 30). As such, NO2 is often used as a marker for road traffic in urban areas. Multiple lines of evidence such as seismic quieting and reduced mobility via location-based services point to changes in traffic-related emissions as the main driver of reductions in NO2 pollution during lockdowns, due to the large proportion of the population working from home (21, 23, 31, 32).Here we exploit the unprecedented changes in human activity unique to the COVID-19 lockdowns and remotely sensed NO2 columns with extraordinary spatial resolution and coverage to understand inequalities in the distribution of NO2 pollution for different racial, ethnic, and socioeconomic subgroups in the United States. Specifically, we address the following: Which demographic subgroups received the largest NO2 reductions? Did the lockdowns grow or shrink the perennial disparities in NO2 pollution across different demographic subgroups? Although the lockdowns are economically unsustainable, how can they advance environmental justice and equity by informing long-term policies to reduce NO2 disparities and the associated public health damages?