Accurate values for polarization discontinuities between pyroelectric materials are critical for understanding and designing the electronic properties of heterostructures. For wurtzite materials, the zincblende structure has been used in the literature as a reference to determine the effective spontaneous polarization constants. We show that, because the zincblende structure has a nonzero formal polarization, this method results in a spurious contribution to the spontaneous polarization differences between materials. In addition, we address the correct choice of “improper” versus “proper” piezoelectric constants. For the technologically important III-nitride materials GaN, AlN, and InN, we determine polarization discontinuities using a consistent reference based on the layered hexagonal structure and the correct choice of piezoelectric constants, and discuss the results in light of available experimental data.

Lattice models of fermions, bosons, and spins have long served to elucidate the essential physics of quantum phase transitions in a variety of systems. Generalizing such models to incorporate driving and dissipation has opened new vistas to investigate nonequilibrium phenomena and dissipative phase transitions in interacting many-body systems. We present a framework for the treatment of such open quantum lattices based on a resummation scheme for the Lindblad perturbation series. Employing a convenient diagrammatic representation, we utilize this method to obtain relevant observables for the open Jaynes-Cummings lattice, a model of special interest for open-system quantum simulation. We demonstrate that the resummation framework allows us to reliably predict observables for both finite and infinite Jaynes-Cummings lattices with different lattice geometries. The resummation of the Lindblad perturbation series can thus serve as a valuable tool in validating open quantum simulators, such as circuit-QED lattices, currently being investigated experimentally.

Nematicity and magnetism are two key features in Fe-based superconductors, and their interplay is one of the most important unsolved problems. In FeSe, the magnetic order is absent below the structural transition temperature $T_{\mathrm{str}}=90\mathrm{K}$, in stark contrast to the fact that the magnetism emerges slightly below $T_{\mathrm{str}}$ in other families. To understand such amazing material dependence, we investigate the spin-fluctuation-mediated orbital order ($n_{xz}\ne n_{yz}$) by focusing on the orbital-spin interplay driven by the strong-coupling effect, called the vertex correction. This orbital-spin interplay is very strong in FeSe because of the small ratio between the Hund’s and Coulomb interactions ($\overline{J}/\overline{U}$) and large $d_{xz}$, $d_{yz}$-orbital weight at the Fermi level. For this reason, in the FeSe model, the orbital order is established irrespective of the fact that the spin fluctuations are very weak, so the magnetism is absent below $T_{\mathrm{str}}$. In contrast, in the LaFeAsO model, the magnetic order appears just below $T_{\mathrm{str}}$ both experimentally and theoretically. Thus, the orbital-spin interplay due to the vertex correction is the key ingredient in understanding the rich phase diagram with nematicity and magnetism in Fe-based superconductors in a unified way.

We report on a detailed experimental investigation of the equation of state (EoS) of the three-dimensional Fermi-Hubbard model (FHM) in its generalized $\mathrm{SU}(N)$-symmetric form, using a degenerate ytterbium gas in an optical lattice. In its more common spin-$1/2$ form, the FHM is a central model of condensed-matter physics. The generalization to $N>2$ was first used to describe multi-orbital materials and is expected to exhibit novel many-body phases in a complex phase diagram. By realizing and locally probing the $\mathrm{SU}(N)$ FHM with ultracold atoms, we obtain model-free access to thermodynamic quantities. The measurement of the EoS and the local compressibility allows us to characterize the crossover from a compressible metal to an incompressible Mott insulator. We reach specific entropies above Néel order but below that of uncorrelated spins. Having access to the EoS of such a system represents an important step towards probing predicted novel $\mathrm{SU}(N)$ phases.

The direct transition from an insulator to a superconductor (SC) in Fermi systems is a problem of long-standing interest, which necessarily goes beyond the standard BCS paradigm of superconductivity as a Fermi surface instability. We introduce here a simple, translationally invariant lattice fermion model that undergoes a SC-insulator transition (SIT) and elucidate its properties using analytical methods and quantum Monte Carlo simulations. We show that there is a fermionic band insulator to bosonic insulator crossover in the insulating phase and a BCS-to-BEC crossover in the SC. The SIT is always found to be from a bosonic insulator to a BEC-like SC, with an energy gap for fermions that remains finite across the SIT. The energy scales that go critical at the SIT are the gap to pair excitations in the insulator and the superfluid stiffness in the SC. In addition to giving insight into important questions about the SIT in solid-state systems, our model should be experimentally realizable using ultracold fermions in optical lattices.

Real-life quantum computers are inevitably affected by intrinsic noise resulting in dissipative nonunitary dynamics realized by these devices. We consider an open-system quantum annealing algorithm optimized for such a realistic analog quantum device which takes advantage of noise-induced thermalization and relies on incoherent quantum tunneling at finite temperature. We theoretically analyze the performance of this algorithm considering a $p$-spin model that allows for a mean-field quasiclassical solution and, at the same time, demonstrates the first-order phase transition and exponential degeneracy of states, typical characteristics of spin glasses. We demonstrate that finite-temperature effects introduced by the noise are particularly important for the dynamics in the presence of the exponential degeneracy of metastable states. We determine the optimal regime of the open-system quantum annealing algorithm for this model and find that it can outperform simulated annealing in a range of parameters. Large-scale multiqubit quantum tunneling is instrumental for the quantum speedup in this model, which is possible because of the unusual nonmonotonous temperature dependence of the quantum-tunneling action in this model, where the most efficient transition rate corresponds to zero temperature. This model calculation is the first analytically tractable example where open-system quantum annealing algorithm outperforms simulated annealing, which can, in principle, be realized using an analog quantum computer.

Coherent scattering of light from ultracold atoms involves an exchange of energy and momentum introducing a wealth of nonlinear dynamical phenomena. As a prominent example, particles can spontaneously form stationary periodic configurations that simultaneously maximize the light scattering and minimize the atomic potential energy in the emerging optical lattice. Such self-ordering effects resulting in periodic lattices via bimodal symmetry breaking have been experimentally observed with cold gases and Bose-Einstein condensates (BECs) inside an optical resonator. Here, we study a new regime of periodic pattern formation for an atomic BEC in free space, driven by far off-resonant counterpropagating and noninterfering lasers of orthogonal polarization. In contrast to previous works, no spatial light modes are preselected by any boundary conditions and the transition from homogeneous to periodic order amounts to a crystallization of both light and ultracold atoms breaking a continuous translational symmetry. In the crystallized state the BEC acquires a phase similar to a supersolid with an emergent intrinsic length scale whereas the light field forms an optical lattice allowing phononic excitations via collective backscattering, which are gapped due to the infinte-range interactions. The system we study constitutes a novel configuration allowing the simulation of synthetic solid-state systems with ultracold atoms including long-range phonon dynamics.

In monolayers of semiconducting transition metal dichalcogenides, the light helicity (${\sigma }^{+}$ or ${\sigma }^{-}$) is locked to the valley degree of freedom, leading to the possibility of optical initialization of distinct valley populations. However, an extremely rapid valley pseudospin relaxation (at the time scale of picoseconds) occurring for optically bright (electric-dipole active) excitons imposes some limitations on the development of opto-valleytronics. Here, we show that valley pseudospin relaxation of excitons can be significantly suppressed in a ${\mathrm{WSe}}_2$ monolayer, a direct-gap two-dimensional semiconductor with the exciton ground state being optically dark. We demonstrate that the already inefficient relaxation of the exciton pseudospin in such a system can be suppressed even further by the application of a tiny magnetic field of about 100 mT. Time-resolved spectroscopy reveals the pseudospin dynamics to be a two-step relaxation process. An initial decay of the pseudospin occurs at the level of dark excitons on a time scale of 100 ps, which is tunable with a magnetic field. This decay is followed by even longer decay ($>1\mathrm{ns}$), once the dark excitons form more complex pseudo-particles allowing for their radiative recombination. Our findings of slow valley pseudospin relaxation easily manipulated by the magnetic field open new prospects for engineering the dynamics of the valley pseudospin in transition metal dichalcogenides.

Despite significant progress in resonant inelastic x-ray scattering (RIXS) experiments on cuprates at the Cu $L$-edge, a theoretical understanding of the cross section remains incomplete in terms of elementary excitations and the connection to both charge and spin structure factors. Here, we use state-of-the-art, unbiased numerical calculations to study the low-energy excitations probed by RIXS in the Hubbard model, relevant to the cuprates. The results highlight the importance of scattering geometry, in particular, both the incident and scattered x-ray photon polarization, and they demonstrate that on a qualitative level the RIXS spectral shape in the cross-polarized channel approximates that of the spin dynamical structure factor. However, in the parallel-polarized channel, the complexity of the RIXS process beyond a simple two-particle response complicates the analysis and demonstrates that approximations and expansions that attempt to relate RIXS to less complex correlation functions cannot reproduce the full diversity of RIXS spectral features.

Two-dimensional topological insulators with a large bulk band gap are promising for experimental studies of quantum spin Hall effect and for spintronic device applications. Despite considerable theoretical efforts in predicting large-gap two-dimensional topological insulator candidates, none of them have been experimentally demonstrated to have a full gap, which is crucial for quantum spin Hall effect. Here, by combining scanning tunneling microscopy/spectroscopy and angle-resolved photoemission spectroscopy, we reveal that ${\mathrm{ZrTe}}_5$ crystal hosts a large full gap of $\sim 100\mathrm{meV}$ on the surface and a nearly constant density of states within the entire gap at the monolayer step edge. These features are well reproduced by our first-principles calculations, which point to the topologically nontrivial nature of the edge states.

We derive a bulk-boundary correspondence for three-dimensional (3D) symmetry-protected topological phases with unitary symmetries. The correspondence consists of three equations that relate bulk properties of these phases to properties of their gapped, symmetry-preserving surfaces. Both the bulk and surface data appearing in our correspondence are defined via a procedure in which we gauge the symmetries of the system of interest and then study the braiding statistics of excitations of the resulting gauge theory. The bulk data are defined in terms of the statistics of bulk excitations, while the surface data are defined in terms of the statistics of surface excitations. An appealing property of these data is that it is plausibly complete in the sense that the bulk data uniquely distinguish each 3D symmetry-protected topological phase, while the surface data uniquely distinguish each gapped, symmetric surface. Our correspondence applies to any 3D bosonic symmetry-protected topological phase with finite Abelian unitary symmetry group. It applies to any surface that (1) supports only Abelian anyons and (2) has the property that the anyons are not permuted by the symmetries.

We show that two-dimensional periodically driven quantum systems with spatial disorder admit a unique topological phase, which we call the anomalous Floquet-Anderson insulator (AFAI). The AFAI is characterized by a quasienergy spectrum featuring chiral edge modes coexisting with a fully localized bulk. Such a spectrum is impossible for a time-independent, local Hamiltonian. These unique characteristics of the AFAI give rise to a new topologically protected nonequilibrium transport phenomenon: quantized, yet nonadiabatic, charge pumping. We identify the topological invariants that distinguish the AFAI from a trivial, fully localized phase, and show that the two phases are separated by a phase transition.

We classify insulators by generalized symmetries that combine space-time transformations with quasimomentum translations. Our group-cohomological classification generalizes the nonsymmorphic space groups, which extend point groups by real-space translations; i.e., nonsymmorphic symmetries unavoidably translate the spatial origin by a fraction of the lattice period. Here, we further extend nonsymmorphic groups by reciprocal translations, thus placing real and quasimomentum space on equal footing. We propose that group cohomology provides a symmetry-based classification of quasimomentum manifolds, which in turn determines the band topology. In this sense, cohomology underlies band topology. Our claim is exemplified by the first theory of time-reversal-invariant insulators with nonsymmorphic spatial symmetries. These insulators may be described as “piecewise topological,” in the sense that subtopologies describe the different high-symmetry submanifolds of the Brillouin zone, and the various subtopologies must be pieced together to form a globally consistent topology. The subtopologies that we discover include a glide-symmetric analog of the quantum spin Hall effect, an hourglass-flow topology (exemplified by our recently proposed KHgSb material class), and quantized non-Abelian polarizations. Our cohomological classification results in an atypical bulk-boundary correspondence for our topological insulators.

Carrying out fault-tolerant topological quantum computation using non-Abelian anyons (e.g., Majorana zero modes) is currently an important goal of worldwide experimental efforts. However, the Gottesman-Knill theorem [1] holds that if a system can only perform a certain subset of available quantum operations (i.e., operations from the Clifford group) in addition to the preparation and detection of qubit states in the computational basis, then that system is insufficient for universal quantum computation. Indeed, any measurement results in such a system could be reproduced within a local hidden variable theory, so there is no need for a quantum-mechanical explanation and therefore no possibility of quantum speedup [2]. Unfortunately, Clifford operations are precisely the ones available through braiding and measurement in systems supporting non-Abelian Majorana zero modes, which are otherwise an excellent candidate for topologically protected quantum computation. In order to move beyond the classically simulable subspace, an additional phase gate is required. This phase gate allows the system to violate the Bell-like Clauser-Horne-Shimony-Holt (CHSH) inequality that would constrain a local hidden variable theory. In this article, we introduce a new type of phase gate for the already-existing semiconductor-based Majorana wire systems and demonstrate how this phase gate may be benchmarked using CHSH measurements. We present an experimentally feasible schematic for such an experiment using a “measurement-only” approach that bypasses the need for explicit Majorana braiding. This approach may be scaled beyond the two-qubit system necessary for CHSH violations, leading to a well-defined platform for universal fault-tolerant quantum computation using Majorana zero modes.

The Seebeck coefficient $S$ of the cuprate superconductor ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ (LSCO) was measured in magnetic fields large enough to access the normal state at low temperatures, for a range of Sr concentrations from $x=0.07$ to $x=0.15$. For $x=0.11$, 0.12, 0.125, and 0.13, $S/T$ decreases upon cooling to become negative at low temperatures. The same behavior is observed in the Hall coefficient $R_{\mathrm{H}}(T)$. In analogy with other hole-doped cuprates at similar hole concentrations $p$, the negative $S$ and $R_{\mathrm{H}}$ show that the Fermi surface of LSCO undergoes a reconstruction caused by the onset of charge-density-wave modulations. Such modulations have indeed been detected in LSCO by x-ray diffraction in precisely the same doping range. Our data show that in LSCO this Fermi-surface reconstruction is confined to $0.085<p<0.15$. We argue that in the field-induced normal state of LSCO, charge-density-wave order ends at a critical doping $p_{\mathrm{CDW}}=0.15\pm 0.005$, well below the pseudogap critical doping $p^{\star }\simeq 0.19$.

The electron-phonon coupling and the corresponding energy exchange are investigated experimentally and by ab initio theory in nonequilibrium states of the free-electron metal aluminium. The temporal evolution of the atomic mean-squared displacement in laser-excited thin freestanding films is monitored by femtosecond electron diffraction. The electron-phonon coupling strength is obtained for a range of electronic and lattice temperatures from density functional theory molecular dynamics simulations. The electron-phonon coupling parameter extracted from the experimental data in the framework of a two-temperature model (TTM) deviates significantly from the ab initio values. We introduce a nonthermal lattice model (NLM) for describing nonthermal phonon distributions as a sum of thermal distributions of the three phonon branches. The contributions of individual phonon branches to the electron-phonon coupling are considered independently and found to be dominated by longitudinal acoustic phonons. Using all material parameters from first-principles calculations except the phonon-phonon coupling strength, the prediction of the energy transfer from electrons to phonons by the NLM is in excellent agreement with time-resolved diffraction data. Our results suggest that the TTM is insufficient for describing the microscopic energy flow even for simple metals like aluminium and that the determination of the electron-phonon coupling constant from time-resolved experiments by means of the TTM leads to incorrect values. In contrast, the NLM describing transient phonon populations by three parameters appears to be a sufficient model for quantitatively describing electron-lattice equilibration in aluminium. We discuss the general applicability of the NLM and provide a criterion for the suitability of the two-temperature approximation for other metals.

We present an analytical approach for bond percolation on multiplex networks and use it to determine the expected size of the giant connected component and the value of the critical bond occupation probability in these networks. We advocate the relevance of these tools to the modeling of multilayer robustness and contribute to the debate on whether any benefit is to be yielded from studying a full multiplex structure as opposed to its monoplex projection, especially in the seemingly irrelevant case of a bond occupation probability that does not depend on the layer. Although we find that in many cases the predictions of our theory for multiplex networks coincide with previously derived results for monoplex networks, we also uncover the remarkable result that for a certain class of multiplex networks, well described by our theory, new critical phenomena occur as multiple percolation phase transitions are present. We provide an instance of this phenomenon in a multiplex network constructed from London rail and European air transportation data sets.

We study possible quantum $U(1)$ spin liquids in three dimensions with time-reversal symmetry. We find a total of seven families of such $U(1)$ spin liquids, distinguished by the properties of their emergent electric or magnetic charges. We show how these spin liquids are related to each other. Two of these classes admit nontrivial protected surface states which we describe. We show how to access all of the seven spin liquids through slave particle (parton) constructions. We also provide intuitive loop gas descriptions of their ground-state wave functions. One of these phases is the “topological Mott insulator,” conventionally described as a topological insulator of an emergent fermionic “spinon.” We show that this phase admits a remarkable dual description as a topological insulator of emergent fermionic magnetic monopoles. This results in a new (possibly natural) surface phase for the topological Mott insulator and a new slave particle construction. We describe some of the continuous quantum phase transitions between the different $U(1)$ spin liquids. Each of these seven families of states admits a finer distinction in terms of their surface properties, which we determine by combining these spin liquids with symmetry-protected topological phases. We discuss lessons for materials such as pyrochlore quantum spin ices which may harbor a $U(1)$ spin liquid. We suggest the topological Mott insulator as a possible ground state in some range of parameters for the quantum spin ice Hamiltonian.

Three-dimensional orientational order in systems whose ground states possess nonzero gradients typically exhibits linelike structures or defects: $\lambda$ lines in cholesterics or Skyrmion tubes in ferromagnets, for example. Here, we show that such lines can be identified as a set of natural geometric singularities in a unit vector field, the generalization of the umbilic points of a surface. We characterize these lines in terms of the natural vector bundles that the order defines and show that they give a way to localize and identify Skyrmion distortions in chiral materials—in particular, that they supply a natural representative of the Poincaré dual of the cocycle describing the topology. Their global structure leads to the definition of a self-linking number and helicity integral which relates the linking of umbilic lines to the Hopf invariant of the texture.

The metal-insulator transition has been a subject of intense research since Mott first proposed that the metallic behavior of interacting electrons could turn to an insulating one as electron correlations increase. Here, we consider electrons with massless Dirac-like dispersion in two spatial dimensions, described by the Hubbard models on two geometrically different lattices, and perform numerically exact calculations on unprecedentedly large systems that, combined with a careful finite-size scaling analysis, allow us to explore the quantum critical behavior in the vicinity of the interaction-driven metal-insulator transition. Thereby, we find that the transition is continuous, and we determine the quantum criticality for the corresponding universality class, which is described in the continuous limit by the Gross-Neveu model, a model extensively studied in quantum field theory. Furthermore, we discuss a fluctuation-driven scenario for the metal-insulator transition in the interacting Dirac electrons: The metal-insulator transition is triggered only by the vanishing of the quasiparticle weight, not by the Dirac Fermi velocity, which instead remains finite near the transition. This important feature cannot be captured by a simple mean-field or Gutzwiller-type approximate picture but is rather consistent with the low-energy behavior of the Gross-Neveu model.