There is strong experimental evidence that the superconductor ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ has a chiral $p$-wave order parameter. This symmetry does not require that the associated gap has nodes, yet specific heat, ultrasound, and thermal conductivity measurements indicate the presence of nodes in the superconducting gap structure of ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$. Theoretical scenarios have been proposed to account for the existence of deep minima or accidental nodes (minima tuned to zero or below by material parameters) within a $p$-wave state. Other scenarios propose chiral $d$-wave and $f$-wave states, with horizontal and vertical line nodes, respectively. To elucidate the nodal structure of the gap, it is essential to know whether the lines of nodes (or minima) are vertical (parallel to the tetragonal $c$ axis) or horizontal (perpendicular to the $c$ axis). Here, we report thermal conductivity measurements on single crystals of ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ down to 50 mK for currents parallel and perpendicular to the $c$ axis. We find that there is substantial quasiparticle transport in the $T=0$ limit for both current directions. A magnetic field $H$ immediately excites quasiparticles with velocities both in the basal plane and in the $c$ direction. Our data down to $T_c/30$ and down to $H_{c2}/100$ show no evidence that the nodes are in fact deep minima. Relative to the normal state, the thermal conductivity of the superconducting state is found to be very similar for the two current directions, from $H=0$ to $H=H_{c2}$. These findings show that the gap structure of ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ consists of vertical line nodes. This rules out a chiral $d$-wave state. Given that the $c$-axis dispersion (warping) of the Fermi surface in ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ varies strongly from sheet to sheet, the small $a-c$ anisotropy suggests that the line nodes are present on all three sheets of the Fermi surface. If imposed by symmetry, vertical line nodes would be inconsistent with a $p$-wave order parameter for ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$. To reconcile the gap structure revealed by our data with a $p$-wave state, a mechanism must be found that produces accidental line nodes in ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$.

A broad range of membrane proteins display anomalous diffusion on the cell surface. Different methods provide evidence for obstructed subdiffusion and diffusion on a fractal space, but the underlying structure inducing anomalous diffusion has never been visualized because of experimental challenges. We addressed this problem by imaging the cortical actin at high resolution while simultaneously tracking individual membrane proteins in live mammalian cells. Our data confirm that actin introduces barriers leading to compartmentalization of the plasma membrane and that membrane proteins are transiently confined within actin fences. Furthermore, superresolution imaging shows that the cortical actin is organized into a self-similar meshwork. These results present a hierarchical nanoscale picture of the plasma membrane.

The strong coupling limit of cavity quantum electrodynamics (QED) implies the capability of a matterlike quantum system to coherently transform an individual excitation into a single photon within a resonant structure. This not only enables essential processes required for quantum information processing but also allows for fundamental studies of matter-light interaction. In this work, we demonstrate strong coupling between the charge degree of freedom in a gate-defined GaAs double quantum dot (DQD) and a frequency-tunable high impedance resonator realized using an array of superconducting quantum interference devices. In the resonant regime, we resolve the vacuum Rabi mode splitting of size $2g/2\pi =238\mathrm{MHz}$ at a resonator linewidth $\kappa /2\pi =12\mathrm{MHz}$ and a DQD charge qubit decoherence rate of ${\gamma }_2/2\pi =40\mathrm{MHz}$ extracted independently from microwave spectroscopy in the dispersive regime. Our measurements indicate a viable path towards using circuit-based cavity QED for quantum information processing in semiconductor nanostructures.

Active matter exemplified by suspensions of motile bacteria or synthetic self-propelled particles exhibits a remarkable propensity to self-organization and collective motion. The local input of energy and simple particle interactions often lead to complex emergent behavior manifested by the formation of macroscopic vortices and coherent structures with long-range order. A realization of an active system has been conceived by combining swimming bacteria and a lyotropic liquid crystal. Here, by coupling the well-established and validated model of nematic liquid crystals with the bacterial dynamics, we develop a computational model describing intricate properties of such a living nematic. In faithful agreement with the experiment, the model reproduces the onset of periodic undulation of the director and consequent proliferation of topological defects with the increase in bacterial concentration. It yields a testable prediction on the accumulation of bacteria in the cores of $+1/2$ topological defects and depletion of bacteria in the cores of $-1/2$ defects. Our dedicated experiment on motile bacteria suspended in a freestanding liquid crystalline film fully confirms this prediction. Our findings suggest novel approaches for trapping and transport of bacteria and synthetic swimmers in anisotropic liquids and extend a scope of tools to control and manipulate microscopic objects in active matter.

The emergent cooperative behavior of mobile physical entities exchanging information with their neighborhood has become an important problem across disciplines, thus requiring a general framework to describe such a variety of situations. We introduce a generic model to tackle this problem by considering the synchronization in time-evolving networks generated by the stochastic motion of self-propelled physical interacting units. This framework generalizes previous approaches and brings a unified picture to understand the role played by the network topology, the motion of the agents, and their mutual interaction. This allows us to identify different dynamic regimes where synchronization can be understood from theoretical considerations. While for noninteracting particles, self-propulsion accelerates synchronization, the presence of excluded volume interactions gives rise to a richer scenario, where self-propulsion has a nonmonotonic impact on synchronization. We show that the synchronization of locally coupled mobile oscillators generically proceeds through coarsening, verifying the dynamic scaling hypothesis, with the same scaling laws as the 2D $XY$ model following a quench. Our results shed light into the generic nature of synchronization in time-dependent networks, providing an efficient way to understand more specific situations involving interacting mobile agents.

A new type of topological state in strongly correlated condensed matter systems, the heavy Weyl fermion state, has been found in a heavy fermion material, ${\mathrm{CeRu}}_4{\mathrm{Sn}}_6$, which has no inversion symmetry. Two different types of Weyl points, types I and II, can be found in the quasiparticle band structure obtained by the $\mathrm{LDA}+\mathrm{Gutzwiller}$ calculations, which can treat the strong correlation effects among the $f$ electrons from cerium atoms. The surface calculations indicate that the topologically protected Fermi arc states exist on the (010) but not on the (001) surface.

In a periodically driven (Floquet) system, there is the possibility for new phases of matter, not present in stationary systems, protected by discrete time-translation symmetry. This includes topological phases protected in part by time-translation symmetry, as well as phases distinguished by the spontaneous breaking of this symmetry, dubbed “Floquet time crystals.” We show that such phases of matter can exist in the prethermal regime of periodically driven systems, which exists generically for sufficiently large drive frequency, thereby eliminating the need for integrability or strong quenched disorder, which limited previous constructions. We prove a theorem that states that such a prethermal regime persists until times that are nearly exponentially long in the ratio of certain couplings to the drive frequency. By similar techniques, we can also construct stationary systems that spontaneously break continuous time-translation symmetry. Furthermore, we argue that for driven systems coupled to a cold bath, the prethermal regime could potentially persist to infinite time.

The long-standing and controversial Fermi-Pasta-Ulam problem addresses fundamental issues of statistical physics, and the attempt to resolve the mystery of the recurrences has led to many great discoveries, such as chaos, integrable systems, and soliton theory. From a general perspective, the recurrence is commonly considered as a coherent phase-sensitive effect that originates in the property of integrability of the system. In contrast to this interpretation, we show that convection among a pair of waves is responsible for a new recurrence phenomenon that takes place for strongly incoherent waves far from integrability. We explain the incoherent recurrence by developing a nonequilibrium spatiotemporal kinetic formulation that accounts for the existence of phase correlations among incoherent waves. The theory reveals that the recurrence originates in a novel form of modulational instability, which shows that strongly correlated fluctuations are spontaneously created among the random waves. Contrary to conventional incoherent modulational instabilities, we find that Landau damping can be completely suppressed, which unexpectedly removes the threshold of the instability. Consequently, the recurrence can take place for strongly incoherent waves and is thus characterized by a reduction of nonequilibrium entropy that violates the $H$ theorem of entropy growth. In its long-term evolution, the system enters a secondary turbulent regime characterized by an irreversible process of relaxation to equilibrium. At variance with the expected thermalization described by standard Gibbsian statistical mechanics, our thermalization process is not dictated by the usual constraints of energy and momentum conservation: The inverse temperatures associated with energy and momentum are zero. This unveils a previously unrecognized scenario of unconstrained thermalization, which is relevant to a variety of weakly dispersive wave systems. Our work should stimulate the development of new experiments aimed at observing recurrence behaviors with random waves. From a broader perspective, the spatiotemporal kinetic formulation we develop here paves the way to the study of novel forms of global incoherent collective behaviors in wave turbulence, such as the formation of incoherent breather structures.

The search for a simple description of fundamental physical processes is an important part of quantum theory. One example for such an abstraction can be found in the distance lab paradigm: if two separated parties are connected via a classical channel, it is notoriously difficult to characterize all possible operations these parties can perform. This class of operations is widely known as local operations and classical communication. Surprisingly, the situation becomes comparably simple if the more general class of separable operations is considered, a finding that has been extensively used in quantum information theory for many years. Here, we propose a related approach for the resource theory of quantum coherence, where two distant parties can perform only measurements that do not create coherence and can communicate their outcomes via a classical channel. We call this class local incoherent operations and classical communication. While the characterization of this class is also difficult in general, we show that the larger class of separable incoherent operations has a simple mathematical form, yet still preserves the main features of local incoherent operations and classical communication. We demonstrate the relevance of our approach by applying it to three different tasks: assisted coherence distillation, quantum teleportation, and single-shot quantum state merging. We expect that the results we obtain in this work also transfer to other concepts of coherence that are discussed in recent literature. The approach we present here opens new ways to study the resource theory of coherence in distributed scenarios.

The synthesis of transition metal heterostructures is currently one of the most vivid fields in the design of novel functional materials. In this paper, we propose a simple scheme to predict band alignment and charge transfer in complex oxide interfaces. For semiconductor heterostructures, band-alignment rules like the well-known Anderson or Schottky-Mott rule are based on comparison of the work function or electron affinity of the bulk components. This scheme breaks down for oxides because of the invalidity of a single work-function approximation as recently shown in [Phys. Rev. B 93, 235116 (2016); Adv. Funct. Mater. 26, 5471 (2016)]. Here, we propose a new scheme that is built on a continuity condition of valence states originating in the compounds’ shared network of oxygen. It allows for the prediction of sign and relative amplitude of the intrinsic charge transfer, taking as input only information about the bulk properties of the components. We support our claims by numerical density functional theory simulations as well as (where available) experimental evidence. Specific applications include (i) controlled doping of ${\mathrm{SrTiO}}_3$ layers with the use of $4d$ and $5d$ transition metal oxides and (ii) the control of magnetic ordering in manganites through tuned charge transfer.

We discuss Bragg scattering on both Bose and Fermi gases with strong short-range interactions in the deep inelastic regime of large wave vector transfer $q$, where the dynamic structure factor is dominated by a resonance near the free-particle energy $\hslash \omega ={ϵ}_{\mathbf{q}}={\hslash }^2{q}^2/2m$. Using a systematic short-distance expansion, the structure factor at high momentum is shown to exhibit a nontrivial dependence on frequency characterized by two separate scaling regimes. First, for frequencies that differ from the single-particle energy by terms of order $\mathcal{O}(q)$ (i.e., small deviations compared to the single-particle energy), the dynamic structure factor is described by the impulse approximation of Hohenberg and Platzman. Second, deviations of order $\mathcal{O}(q^2)$ (i.e., of the same order or larger than the single-particle energy) are described by the operator product expansion, with a universal crossover connecting both regimes. The scaling is consistent with the leading asymptotics for a number of sum rules in the large momentum limit. Furthermore, we derive an exact expression for the shift and width of the single-particle peak at large momentum due to interactions, thus extending a result by Beliaev [J. Exp. Theor. Phys. 7, 299 (1958)] for the low-density Bose gas to arbitrary values of the scattering length $a$. The shift exhibits a maximum around $qa\simeq 1$, which is connected with a maximum in the static structure factor due to strong short-range correlations. For Bose gases with moderate interaction strengths, the theoretically predicted shift is consistent with the value observed by Papp et al. [Phys. Rev. Lett. 101, 135301 (2008)]. Finally, we develop a diagrammatic theory for the dynamic structure factor which accounts for the correlations beyond Bogoliubov theory. It covers the full range of momenta and frequencies and provides an explicit example for the emergence of asymptotic scaling at large momentum.

We present a systematic, perturbative method for correcting quantum gates to suppress errors that take the target system out of a chosen subspace. Our method addresses the generic problem of nonadiabatic errors in adiabatic evolution and state preparation, as well as general leakage errors due to spurious couplings to undesirable states. The method is based on the Magnus expansion: By correcting control pulses, we modify the Magnus expansion of an initially given, imperfect unitary in such a way that the desired evolution is obtained. Applications to adiabatic quantum state transfer, superconducting qubits, and generalized Landau-Zener problems are discussed.

We consider symmetry-protected topological (SPT) phases with crystalline point group symmetry, dubbed point group SPT (pgSPT) phases. We show that such phases can be understood in terms of lower-dimensional topological phases with on-site symmetry and that they can be constructed as stacks and arrays of these lower-dimensional states. This provides the basis for a general framework to classify and characterize bosonic and fermionic pgSPT phases, which can be applied for arbitrary crystalline point group symmetry and in arbitrary spatial dimensions. We develop and illustrate this framework by means of a few examples, focusing on three-dimensional states. We classify bosonic pgSPT phases and fermionic topological crystalline superconductors with ${\mathbb{Z}}_2^P$ (reflection) symmetry, electronic topological crystalline insulators (TCIs) with $\mathrm{U}(1)\times {\mathbb{Z}}_2^P$ symmetry, and bosonic pgSPT phases with $C_{2v}$ symmetry, which is generated by two perpendicular mirror reflections. We also study surface properties, with a focus on gapped, topologically ordered surface states. For electronic TCIs, we find a ${\mathbb{Z}}_8\times {\mathbb{Z}}_2$ classification, where the ${\mathbb{Z}}_8$ corresponds to known states obtained from noninteracting electrons, and the ${\mathbb{Z}}_2$ corresponds to a “strongly correlated” TCI that requires strong interactions in the bulk. Our approach may also point the way toward a general theory of symmetry-enriched topological phases with crystalline point group symmetry.

We study the statistics of infima, stopping times, and passage probabilities of entropy production in nonequilibrium steady states, and we show that they are universal. We consider two examples of stopping times: first-passage times of entropy production and waiting times of stochastic processes, which are the times when a system reaches a given state for the first time. Our main results are as follows: (i) The distribution of the global infimum of entropy production is exponential with mean equal to minus Boltzmann’s constant; (ii) we find exact expressions for the passage probabilities of entropy production; (iii) we derive a fluctuation theorem for stopping-time distributions of entropy production. These results have interesting implications for stochastic processes that can be discussed in simple colloidal systems and in active molecular processes. In particular, we show that the timing and statistics of discrete chemical transitions of molecular processes, such as the steps of molecular motors, are governed by the statistics of entropy production. We also show that the extreme-value statistics of active molecular processes are governed by entropy production; for example, we derive a relation between the maximal excursion of a molecular motor against the direction of an external force and the infimum of the corresponding entropy-production fluctuations. Using this relation, we make predictions for the distribution of the maximum backtrack depth of RNA polymerases, which follow from our universal results for entropy-production infima.

We investigate many-body dynamics in a one-dimensional interacting periodically driven system, based on a partially filled version of Thouless’s topologically quantized adiabatic pump. The corresponding single-particle Floquet bands are chiral, with the Floquet spectrum realizing nontrivial cycles around the quasienergy Brillouin zone. For generic filling, with either bosons or fermions, the system is gapless and is expected to rapidly absorb energy from the driving field. We identify parameter regimes where scattering between Floquet bands of opposite chirality is exponentially suppressed, opening a long time window in which the system prethermalizes to an infinite-temperature state restricted to a single Floquet band. In this quasi-steady state, the time-averaged current takes a universal value determined solely by the density of particles and the topological winding number of the populated Floquet band. This remarkable behavior may be readily studied experimentally in recently developed cold atom systems.

Electrides are intrinsic electron-rich materials enabling applications as excellent electron emitters, superior catalysts, and strong reducing agents. There are a number of organic electrides; however, their instability at room temperature and sensitivity to moisture are bottlenecks for their practical uses. Known inorganic electrides are rare, but they appear to have greater thermal stability at ambient conditions and are thus better characterized for application. Here, we develop a computer-assisted inverse-design method for searching for a large variety of inorganic electrides unbiased by any known electride structures. It uses the intrinsic property of interstitial electron localization of electrides as the global variable function for swarm intelligence structure searches. We construct two rules of thumb on the design of inorganic electrides pointing to electron-rich ionic systems and low electronegativity of the cationic elements involved. By screening 99 such binary compounds through large-scale computer simulations, we identify 24 stable and 65 metastable new inorganic electrides that show distinct three-, two-, and zero-dimensional conductive properties, among which 18 are existing compounds that have not been pointed to as electrides. Our work reveals the rich abundance of inorganic electrides by providing 33 hitherto unexpected structure prototypes of electrides, of which 19 are not in the known structure databases.

Condensed matter physics has been driven forward by significant experimental and theoretical progress in the study and understanding of equilibrium phase transitions based on symmetry and topology. However, nonequilibrium phase transitions have remained a challenge, in part due to their complexity in theoretical descriptions and the additional experimental difficulties in systematically controlling systems out of equilibrium. Here, we study a one-dimensional chain of 72 microwave cavities, each coupled to a superconducting qubit, and coherently drive the system into a nonequilibrium steady state. We find experimental evidence for a dissipative phase transition in the system in which the steady state changes dramatically as the mean photon number is increased. Near the boundary between the two observed phases, the system demonstrates bistability, with characteristic switching times as long as 60 ms—far longer than any of the intrinsic rates known for the system. This experiment demonstrates the power of circuit QED systems for studying nonequilibrium condensed matter physics and paves the way for future experiments exploring nonequilbrium physics with many-body quantum optics.