Quantum critical scaling at the edge of Fermi liquid stability in a cuprate superconductor

In the high-temperature cuprate superconductors, the pervasiveness of anomalous electronic transport properties suggests that violation of conventional Fermi liquid behavior is closely tied to superconductivity. In other classes of unconventional superconductors, atypical transport is well correlated with proximity to a quantum critical point, but the relative importance of quantum criticality in the cuprates remains uncertain. Here, we identify quantum critical scaling in the electron-doped cuprate material La(2-x)Ce(x)CuO(4) with a line of quantum critical points that surrounds the superconducting phase as a function of magnetic field and charge doping. This zero-temperature phase boundary, which delineates a metallic Fermi liquid regime from an extended non-Fermi liquid ground state, closely follows the upper critical field of the overdoped superconducting phase and gives rise to an expanse of distinct non-Fermi liquid behavior at finite temperatures. Together with signatures of two distinct flavors of quantum fluctuations, these facts suggest that quantum criticality plays a significant role in shaping the anomalous properties of the cuprate phase diagram.     

Competing ferromagnetism in high-temperature copper oxide superconductors

The extreme variability of observables across the phase diagram of the cuprate high-temperature superconductors has remained a profound mystery, with no convincing explanation for the superconducting dome. Although much attention has been paid to the underdoped regime of the hole-doped cuprates because of its proximity to a complex Mott insulating phase, little attention has been paid to the overdoped regime. Experiments are beginning to reveal that the phenomenology of the overdoped regime is just as puzzling. For example, the electrons appear to form a Landau Fermi liquid, but this interpretation is problematic; any trace of Mott phenomena, as signified by incommensurate antiferromagnetic fluctuations, is absent, and the uniform spin susceptibility shows a ferromagnetic upturn. Here, we show and justify that many of these puzzles can be resolved if we assume that competing ferromagnetic fluctuations are simultaneously present with superconductivity, and the termination of the superconducting dome in the overdoped regime marks a quantum critical point beyond which there should be a genuine ferromagnetic phase at zero temperature. We propose experiments and make predictions to test our theory and suggest that an effort must be mounted to elucidate the nature of the overdoped regime, if the problem of high-temperature superconductivity is to be solved. Our approach places competing order as the root of the complexity of the cuprate phase diagram.     

Field-induced quantum critical route to a Fermi liquid in high-temperature superconductors

In high-transition-temperature (T(c)) superconductivity, charge doping is a natural tuning parameter that takes copper oxides from the antiferromagnet to the superconducting region. In the metallic state above T(c), the standard Landau's Fermi-liquid theory of metals as typified by the temperature squared (T(2)) dependence of resistivity appears to break down. Whether the origin of the non-Fermi-liquid behavior is related to physics specific to the cuprates is a fundamental question still under debate. We uncover a transformation from the non-Fermi-liquid state to a standard Fermi-liquid state driven not by doping but by magnetic field in the overdoped high-T(c) superconductor Tl(2)Ba(2)CuO(6+x). From the c-axis resistivity measured up to 45 T, we show that the Fermi-liquid features appear above a sufficiently high field that decreases linearly with temperature and lands at a quantum critical point near the superconductivity's upper critical field-with the Fermi-liquid coefficient of the T(2) dependence showing a power-law diverging behavior on the approach to the critical point. This field-induced quantum criticality bears a striking resemblance to that in quasi-two-dimensional heavy-Fermion superconductors, suggesting a common underlying spin-related physics in these superconductors with strong electron correlations.     

Thermodynamics of phase formation in the quantum critical metal Sr3Ru2O7

The behavior of matter near zero temperature continuous phase transitions, or "quantum critical points" is a central topic of study in condensed matter physics. In fermionic systems, fundamental questions remain unanswered: the nature of the quantum critical regime is unclear because of the apparent breakdown of the concept of the quasiparticle, a cornerstone of existing theories of strongly interacting metals. Even less is known experimentally about the formation of ordered phases from such a quantum critical "soup." Here, we report a study of the specific heat across the phase diagram of the model system Sr(3)Ru(2)O(7), which features an anomalous phase whose transport properties are consistent with those of an electronic nematic. We show that this phase, which exists at low temperatures in a narrow range of magnetic fields, forms directly from a quantum critical state, and contains more entropy than mean-field calculations predict. Our results suggest that this extra entropy is due to remnant degrees of freedom from the highly entropic state above T(c). The associated quantum critical point, which is "concealed" by the nematic phase, separates two Fermi liquids, neither of which has an identifiable spontaneously broken symmetry, but which likely differ in the topology of their Fermi surfaces.     

Fermi-surface collapse and dynamical scaling near a quantum-critical point

Quantum criticality arises when a macroscopic phase of matter undergoes a continuous transformation at zero temperature. While the collective fluctuations at quantum-critical points are being increasingly recognized as playing an important role in a wide range of quantum materials, the nature of the underlying quantum-critical excitations remains poorly understood. Here we report in-depth measurements of the Hall effect in the heavy-fermion metal YbRh₂Si₂, a prototypical system for quantum criticality. We isolate a rapid crossover of the isothermal Hall coefficient clearly connected to the quantum-critical point from a smooth background contribution; the latter exists away from the quantum-critical point and is detectable through our studies only over a wide range of magnetic field. Importantly, the width of the critical crossover is proportional to temperature, which violates the predictions of conventional theory and is instead consistent with an energy over temperature, E/T, scaling of the quantum-critical single-electron fluctuation spectrum. Our results provide evidence that the quantum-dynamical scaling and a critical Kondo breakdown simultaneously operate in the same material. Correspondingly, we infer that macroscopic scale-invariant fluctuations emerge from the microscopic many-body excitations associated with a collapsing Fermi-surface. This insight is expected to be relevant to the unconventional finite-temperature behavior in a broad range of strongly correlated quantum systems.     

Critical quasiparticle theory applied to heavy fermion metals near an antiferromagnetic quantum phase transition

We use the recently developed critical quasiparticle theory to derive the scaling behavior associated with a quantum critical point in a correlated metal. This is applied to the magnetic-field induced quantum critical point observed in YbRh(2)Si(2), for which we also derive the critical behavior of the specific heat, resistivity, thermopower, magnetization and susceptibility, the Grüneisen coefficient, and the thermal expansion coefficient. The theory accounts very well for the available experimental results.     

Signatures of quantum criticality in pure Cr at high pressure

The elemental antiferromagnet Cr at high pressure presents a new type of naked quantum critical point that is free of disorder and symmetry-breaking fields. Here we measure magnetotransport in fine detail around the critical pressure, P_c ∼ 10 GPa, in a diamond anvil cell and reveal the role of quantum critical fluctuations at the phase transition. As the magnetism disappears and T → 0, the magntotransport scaling converges to a non-mean-field form that illustrates the reconstruction of the magnetic Fermi surface, and is distinct from the critical scaling measured in chemically disordered Cr∶V under pressure. The breakdown of itinerant antiferromagnetism only comes clearly into view in the clean limit, establishing disorder as a relevant variable at a quantum phase transition.     

Anomalous superfluid density in quantum critical superconductors

When a second-order magnetic phase transition is tuned to zero temperature by a nonthermal parameter, quantum fluctuations are critically enhanced, often leading to the emergence of unconventional superconductivity. In these “quantum critical” superconductors it has been widely reported that the normal-state properties above the superconducting transition temperature T_c often exhibit anomalous non-Fermi liquid behaviors and enhanced electron correlations. However, the effect of these strong critical fluctuations on the superconducting condensate below T_c is less well established. Here we report measurements of the magnetic penetration depth in heavy-fermion, iron-pnictide, and organic superconductors located close to antiferromagnetic quantum critical points, showing that the superfluid density in these nodal superconductors universally exhibits, unlike the expected T-linear dependence, an anomalous 3/2 power-law temperature dependence over a wide temperature range. We propose that this noninteger power law can be explained if a strong renormalization of effective Fermi velocity due to quantum fluctuations occurs only for momenta k close to the nodes in the superconducting energy gap Δ(k). We suggest that such “nodal criticality” may have an impact on low-energy properties of quantum critical superconductors.     

Mesoscopic atomic entanglement for precision measurements beyond the standard quantum limit

Squeezing of quantum fluctuations by means of entanglement is a well-recognized goal in the field of quantum information science and precision measurements. In particular, squeezing the fluctuations via entanglement between 2-level atoms can improve the precision of sensing, clocks, metrology, and spectroscopy. Here, we demonstrate 3.4 dB of metrologically relevant squeezing and entanglement for ≳ 10⁵ cold caesium atoms via a quantum nondemolition (QND) measurement on the atom clock levels. We show that there is an optimal degree of decoherence induced by the quantum measurement which maximizes the generated entanglement. A 2-color QND scheme used in this paper is shown to have a number of advantages for entanglement generation as compared with a single-color QND measurement.     

Nervous mechanisms of spontaneous oscillations of systolic blood pressure and heart rate

The phenomenon of rhythmic fluctuations in cardiovascular variables such as heart rate (HR) or arterial blood pressure (BP) has attracted the attention of workers in both pure and applied research. In recent years, the possibility of quantifying these oscillations by using power spectral analysis has aroused a growing interest. We investigated the fluctuations which underly the spontaneous variability of BP and HR in conscious rats. Intrafemoral pulsatile BP was computed to generate evenly spaced signals (systolic, diastolic, mean BP, HR) at 200 ms intervals. This equidistant sampling allowed a direct spectral analysis using a Fast Fourier Transform algorithm. Systolic Blood Pressure (SBP) and HR exhibited low frequency oscillations (Mayer waves, 20-605 mHz) and a high frequency oscillation related to respiration (1,855 mHz). The respiratory fluctuations in HR were almost abolished by vagal blockade (atropine). HR fluctuations in the low frequency regime were diminished by vagal blockade or cardiac sympathetic blockade (atenolol). The respiratory frequency fluctuations in SBP were markedly increased by alpha sympathetic blockade (prazosin). On the contrary the low frequency oscillations in SBP were reduced by alpha sympathetic blockade. These data indicate that in conscious rats: 1) the HR oscillation with respiration is vagally mediated, 2) the HR fluctuation in the low frequency regime is jointly mediated by beta sympathetic and parasympathetic activities, 3) the respiratory oscillation in SBP depends on fluctuations in cardiac output and is normally counteracted by the sympathetic tone, 4) the low frequency oscillations in SBP reflect the sympathetic activity to the resistance vessels.     

Fermi pockets and quantum oscillations of the Hall coefficient in high-temperature superconductors

Recent quantum oscillation measurements in high-temperature superconductors in high magnetic fields and low temperatures have ushered in a new era. These experiments explore the normal state from which superconductivity arises and provide evidence of a reconstructed Fermi surface consisting of electron and hole pockets in a regime in which such a possibility was previously considered to be remote. More specifically, the Hall coefficient has been found to oscillate according to the Onsager quantization condition, involving only fundamental constants and the areas of the pockets, but with a sign that is negative. Here, we explain the observations with the theory that the alleged normal state exhibits a hidden order, the d-density wave, which breaks symmetries signifying time reversal, translation by a lattice spacing, and a rotation by an angle pi/2, while the product of any two symmetry operations is preserved. The success of our analysis underscores the importance of spontaneous breaking of symmetries, Fermi surface reconstruction, and conventional quasiparticles. We primarily focus on the version of the order that is commensurate with the underlying crystalline lattice, but we also touch on the consequences if the order were to incommensurate. It is shown that whereas commensurate order results in two independent oscillation frequencies as a function of the inverse of the applied magnetic field, incommensurate order leads to three independent frequencies. The oscillation amplitudes, however, are determined by the mobilities of the charge carriers comprising the Fermi pockets.     

The inhomogeneous structure of water at ambient conditions

Small-angle X-ray scattering (SAXS) is used to demonstrate the presence of density fluctuations in ambient water on a physical length-scale of ≈1 nm; this is retained with decreasing temperature while the magnitude is enhanced. In contrast, the magnitude of fluctuations in a normal liquid, such as CCl₄, exhibits no enhancement with decreasing temperature, as is also the case for water from molecular dynamics simulations under ambient conditions. Based on X-ray emission spectroscopy and X-ray Raman scattering data we propose that the density difference contrast in SAXS is due to fluctuations between tetrahedral-like and hydrogen-bond distorted structures related to, respectively, low and high density water. We combine our experimental observations to propose a model of water as a temperature-dependent, fluctuating equilibrium between the two types of local structures driven by incommensurate requirements for minimizing enthalpy (strong near-tetrahedral hydrogen-bonds) and maximizing entropy (nondirectional H-bonds and disorder). The present results provide experimental evidence that the extreme differences anticipated in the hydrogen-bonding environment in the deeply supercooled regime surprisingly remain in bulk water even at conditions ranging from ambient up to close to the boiling point.     

Quantum spin correlations through the superconducting-to-normal phase transition in electron-doped superconducting Pr0.88LaCe0.12CuO4-delta

The quantum spin fluctuations of the S = 1/2 Cu ions are important in determining the physical properties of high-transition-temperature (high T(c)) copper oxide superconductors, but their possible role in the electron pairing of superconductivity remains an open question. The principal feature of the spin fluctuations in optimally doped high-T(c) superconductors is a well defined magnetic resonance whose energy (E(R)) tracks T(c) (as the composition is varied) and whose intensity develops like an order parameter in the superconducting state. We show that the suppression of superconductivity and its associated condensation energy by a magnetic field in the electron-doped high-T(c) superconductor Pr(0.88)LaCe(0.12)CuO(4-delta) (T(c) = 24 K), is accompanied by the complete suppression of the resonance and the concomitant emergence of static antiferromagnetic order. Our results demonstrate that the resonance is intimately related to the superconducting condensation energy, and thus suggest that it plays a role in the electron pairing and superconductivity.     

Turning back from the brink: Detecting an impending regime shift in time to avert it

Ecological regime shifts are large, abrupt, long-lasting changes in ecosystems that often have considerable impacts on human economies and societies. Avoiding unintentional regime shifts is widely regarded as desirable, but prediction of ecological regime shifts is notoriously difficult. Recent research indicates that changes in ecological time series (e.g., increased variability and autocorrelation) could potentially serve as early warning indicators of impending shifts. A critical question, however, is whether such indicators provide sufficient warning to adapt management to avert regime shifts. We examine this question using a fisheries model, with regime shifts driven by angling (amenable to rapid reduction) or shoreline development (only gradual restoration is possible). The model represents key features of a broad class of ecological regime shifts. We find that if drivers can only be manipulated gradually management action is needed substantially before a regime shift to avert it; if drivers can be rapidly altered aversive action may be delayed until a shift is underway. Large increases in the indicators only occur once a regime shift is initiated, often too late for management to avert a shift. To improve usefulness in averting regime shifts, we suggest that research focus on defining critical indicator levels rather than detecting change in the indicators. Ideally, critical indicator levels should be related to switches in ecosystem attractors; we present a new spectral density ratio indicator to this end. Averting ecological regime shifts is also dependent on developing policy processes that enable society to respond more rapidly to information about impending regime shifts.     

Manipulating superconducting fluctuations by the Little-Parks-de Gennes effect in ultrasmall Al loops

The destruction of superconducting phase coherence by quantum fluctuations and the control of these fluctuations are a problem of long-standing interest, with recent impetus provided by the relevance of these issues to the pursuit of high temperature superconductivity. Building on the work of Little and Parks, de Gennes predicted more than three decades ago that superconductivity could be destroyed near half-integer-flux quanta in ultrasmall loops, resulting in a destructive regime, and restored by adding a superconducting side branch, which does not affect the flux quantization condition. We report the experimental observation of this Little-Parks-de Gennes effect in Al loops prepared by advanced e-beam lithography. We show that the effect can be used to restore the lost phase coherence by employing side branches.     

Social interactions dominate speed control in poising natural flocks near criticality

Flocks of birds exhibit a remarkable degree of coordination and collective response. It is not just that thousands of individuals fly, on average, in the same direction and at the same speed, but that even the fluctuations around the mean velocity are correlated over long distances. Quantitative measurements on flocks of starlings, in particular, show that these fluctuations are scale-free, with effective correlation lengths proportional to the linear size of the flock. Here we construct models for the joint distribution of velocities in the flock that reproduce the observed local correlations between individuals and their neighbors, as well as the variance of flight speeds across individuals, but otherwise have as little structure as possible. These minimally structured or maximum entropy models provide quantitative, parameter-free predictions for the spread of correlations throughout the flock, and these are in excellent agreement with the data. These models are mathematically equivalent to statistical physics models for ordering in magnets, and the correct prediction of scale-free correlations arises because the parameters—completely determined by the data—are in the critical regime. In biological terms, criticality allows the flock to achieve maximal correlation across long distances with limited speed fluctuations.In a flock of birds, thousands of individuals will fly in the same direction and at the same speed, for long periods of time. However, this average behavior is not enough for flocking to be advantageous. The entire flock must respond to dangers that may be visible only to a small fraction of individuals, requiring information to propagate over long distances. Although it is difficult to measure this information flow directly (1), we know that attacks by predators on a flock have very low success rates (2–4), and that the evasion of predators by starling flocks is associated with the triggering and propagation of waves through the flock (5). Even in the absence of predators, we can see deviations of individual behavior from the average behavior of the flock, and correlations in these fluctuations provide a signature of information flow through the flock. Strikingly, observations on flocks of starlings show that these correlations extend over very long distances, comparable to the size of the flock itself (6).It is generally believed that the interactions among birds in a flock are local—each bird aligns its flight direction and speed to those of its near neighbors (7). If this is correct, then we have to understand how local interactions can generate correlations over much longer distances. In physics, we have two very different mechanisms for local interactions to produce long–ranged correlations. If the system spontaneously breaks a continuous symmetry, for example when all of the spins in a magnet select a particular direction in space along which the macroscopic magnetization will point, then the fluctuations in the system are dominated by Goldstone modes that do not decay on any fixed length scale (8). If we can think of the alignment of flight directions in a flock as being like the alignment of spins in a magnet (9–11), then we can understand the emergence of scale-free correlations via Goldstone’s theorem. We have shown that this is more than a metaphor (12): the minimally structured model consistent with the observed correlations among flight directions of neighboring birds is equivalent to a model of spins in a magnet, and the resulting (parameter-free) prediction of long-ranged correlations among fluctuations in flight direction agrees quantitatively with the data.Not just the fluctuations in flight direction, but also the fluctuations in flight speed are correlated over long distances (6). Now there are no Goldstone modes, because choosing a speed does not correspond to breaking any plausible symmetry of the system. However, there is a second mechanism by which physical systems generate scale-free correlations, and this is by tuning parameters to a critical point (8, 13). As we explore the parameter space of a system (e.g., changing temperature and pressure), we encounter phase transitions, where small changes in parameters produce qualitative changes in behavior of a macroscopic sample (e.g., between liquid and gas). Along the lines in parameter space where these phase transitions exist, there are special points, called “critical points,” where the dependence on parameters becomes, for very large systems, singular but not discontinuous. At these points, fluctuations (e.g., in the density of the liquid) become correlated on all length scales, from the molecular scale of the interactions to the macroscopic scale of the sample as a whole.Tuning to a critical point provides a potential explanation for scale-free correlations in speed of flocking birds, but this is just an analogy; the goal of this paper is to construct a quantitative theory. Our strategy follows ref. 12: we construct the least structured models that are consistent with measured correlations among neighboring birds, and then see if these models can correctly predict the persistence of correlations over much longer distances, comparable to the size of the flock. We will see that this works, and that the underlying mechanism really is the tuning of the system to a critical point. From a biological point of view, this means that individuals in a flock combine individual speed control and social interactions with their neighbors to achieve a maximal range of influence while keeping speed variability low.     

Ultrafast electron crystallography: transient structures of molecules, surfaces, and phase transitions

The static structure of macromolecular assemblies can be mapped out with atomic-scale resolution by using electron diffraction and microscopy of crystals. For transient nonequilibrium structures, which are critical to the understanding of dynamics and mechanisms, both spatial and temporal resolutions are required; the shortest scales of length (0.1-1 nm) and time (10(-13) to 10(-12) s) represent the quantum limit, the nonstatistical regime of rates. Here, we report the development of ultrafast electron crystallography for direct determination of structures with submonolayer sensitivity. In these experiments, we use crystalline silicon as a template for different adsorbates: hydrogen, chlorine, and trifluoroiodomethane. We observe the coherent restructuring of the surface layers with subangstrom displacement of atoms after the ultrafast heat impulse. This nonequilibrium dynamics, which is monitored in steps of 2 ps (total change 相似文献   

Emergence of superconductivity in heavy-electron materials

Although the pairing glue for the attractive quasiparticle interaction responsible for unconventional superconductivity in heavy-electron materials has been identified as the spin fluctuations that arise from their proximity to a magnetic quantum critical point, there has been no model to describe their superconducting transition at temperature T_c that is comparable to that found by Bardeen, Cooper, and Schrieffer (BCS) for conventional superconductors, where phonons provide the pairing glue. Here we propose such a model: a phenomenological BCS-like expression for T_c in heavy-electron materials that is based on a simple model for the effective range and strength of the spin-fluctuation-induced quasiparticle interaction and reflects the unusual properties of the heavy-electron normal state from which superconductivity emerges. We show that it provides a quantitative understanding of the pressure-induced variation of T_c in the “hydrogen atoms” of unconventional superconductivity, CeCoIn₅ and CeRhIn₅, predicts scaling behavior and a dome-like structure for T_c in all heavy-electron quantum critical superconductors, provides unexpected connections between members of this family, and quantifies their variations in T_c with a single parameter.Because the unconventional superconductivity found in many heavy-electron materials arises at the border of antiferromagnetic long-range order, it is natural to consider the possibility that its physical origin is its proximity to a quantum critical point that marks a transition from localized to itinerant behavior, and that the associated magnetic quantum critical spin fluctuations provide the pairing glue (1–5), in contrast to conventional superconductors, where phonons provide the pairing glue (6). However, developing a simple physical picture for the behavior of such quantum critical superconductors, including a Bardeen, Cooper, and Schrieffer (BCS)-like expression for their superconducting transition temperature (T_c), has proven difficult. In part, this is because of the unusual normal state from which superconductivity emerges (7–12), and in part it stems from the difficulty in finding a simple model for an effective frequency-dependent attractive quasiparticle interaction that closely resembles that proposed earlier for the cuprates (13–17).In finding a way to characterize heavy-electron quantum critical superconductivity it is helpful to begin by recalling the principal features of its remarkably similar emergence in two of the best-studied materials, CeCoIn₅ and CeRhIn₅ (18–23). As may be seen in Fig. 1, there are three distinct regions of emergent heavy-electron superconductivity in their pressure–temperature phase diagrams that are defined by a line marking the delocalization cross-over temperature, T_L, at which the collective hybridization of the local moments becomes complete and the Néel temperature, T_N, that marks the onset of long-range antiferromagnetic order of the hybridized local moments.Open in a separate windowFig. 1.A phase diagram for heavy-electron superconductors. In region I, only itinerant heavy electrons exist below T_L owing to complete hybridization of the f-moments with background conduction electrons; in region II, collective hybridization is not complete so that heavy electrons coexist with partially hybridized local moments; in region III, these residual moments order antiferromagnetically (AF) at T_N and the surviving heavy electrons become superconducting (SC) at a lower temperature, T_c. The coupling of heavy electrons to the magnetic spin fluctuations emanating from the QCP is responsible for the superconductivity in all regions.Region I: T_c ≤ T_L. Superconductivity emerges from a fully formed heavy-electron state. The general increase in T_c seen with decreasing pressure is cut off by a competing state, quasiparticle localization, so T_c reaches its maximum value at the pressure, p_L, at which the superconducting and localization transition lines intersect.Region II: T_c > T_L and T_N. Superconductivity emerges from a partially formed heavy-electron state whose ability to superconduct is reduced by the partially hybridized local moments with which it coexists. The region includes the quantum critical point (QCP) at T = 0 that marks a zero temperature transition from a state with partially localized ordered behavior to one that is fully itinerant; this QCP is the origin of the quantum critical spin fluctuations that provide the pairing glue in all three regions (2).Region III: T_c ≤ T_N. Partially hybridized local moments are present in sufficient number to become antiferromagnetically ordered at the Néel temperature T_N despite the presence of coexisting remnant heavy electrons that become superconducting at lower temperatures.The dominance of superconductivity around the QCP supports the idea that the coupling of quantum critical spin fluctuations to the heavy-electron quasiparticles plays a central role, with the resulting induced attractive quasiparticle interaction being maximally effective near it. Importantly, there is direct experimental evidence that these quantum critical fluctuations provide the superconducting glue: Curro et al. (4) find that the spin-lattice relaxation rate, 1/T₁, to which these give rise, scales with T_c at the pressure at which T_c is maximum, whereas a recent detailed investigation of that scaling (5) explains how this comes about. First, at this “optimal” pressure, T_c scales with the coherence temperature, T*, that marks the initial emergence of heavy-electron behavior and is determined by the nearest-neighbor exchange interaction between the f-electron local moments (8); second, at this optimal pressure, 1/T₁ scales with T*, a scaling behavior that is a unique signature of its origin in quantum critical spin fluctuations.In this paper we use these important scaling results to develop a simple BCS-like phenomenological expression for the superconducting transition temperature, show that it explains the variation of T_c with pressure for both CeCoIn₅ and CeRhIn₅, and offer a detailed prediction for a similar dome-like structure in other quantum critical heavy-electron superconductors.     

Critical shape transitions of monolayer lipid domains

Fluorescence microscopy can be used to visualize coexisting fluid phases in lipid monolayers composed of cholesterol and dipalmitoyl phosphatidylcholine under specified conditions of temperature, composition, and lateral pressure. At a critical composition of ≈30 mol% cholesterol, decreasing the average molecular area below a_c [unk]50 Ų per molecule forces the binary mixture through a critical point, where the monolayer becomes homogeneous. At molecular areas ≈10% above this critical area, we observe shape transitions from liquid domains with circular shapes to domains with less symmetrical shapes. Shape transitions and critical shape fluctuations can also be triggered with light, due to photochemical effects on the monolayer. Shape fluctuations of lipid domains can thus be used to sense chemical events at the air-water interface.