We describe the phase diagram of a 2+1-dimensional SU(2) gauge theory of fluctuating incommensurate spin density waves for the hole-doped cuprates. Our primary assumption is that all low-energy fermionic excitations are gauge neutral and electron-like, while the spin density wave order is fractionalized into Higgs fields transforming as adjoints of the gauge SU(2). The confining phase of the gauge theory is a conventional Fermi liquid with a large Fermi surface (and its associated $d$-wave superconductor). There is a quantum phase transition to a Higgs phase describing the “pseudogap” at lower doping. Depending on the quartic terms in the Higgs potential, the Higgs phase exhibits one or more of charge density wave, Ising-nematic, time-reversal odd scalar spin chirality, and ${\mathbb{Z}}_2$ topological orders. It is notable that the emergent broken symmetries in our theory of fluctuating spin density waves coincide with those observed in diverse experiments. For the electron-doped cuprates, the spin density wave fluctuations are at wave vector $(\pi ,\pi )$, and then the corresponding SU(2) gauge theory only has a crossover between the confining and Higgs regimes, with an exponentially large confinement scale deep in the Higgs regime. On the Higgs side, for both the electron- and hole-doped cases, and at scales shorter than the confinement scale (which can be infinite when ${\mathbb{Z}}_2$ topological order is present), the electron spectral function has a “fractionalized Fermi liquid” form with small Fermi surfaces. We also describe the deconfined quantum criticality of the Higgs transition in the limit of a large number of Higgs flavors, and perturbatively discuss its coupling to fermionic excitations.

We establish the existence of a topological classification of many-particle quantum systems undergoing unitary time evolution. The classification naturally inherits phenomenology familiar from equilibrium—it is robust against disorder and interactions, and exhibits a nonequilibrium bulk-boundary correspondence, which connects bulk topological properties to the entanglement spectrum. We explicitly construct a nonequilibrium classification of noninteracting fermionic systems with nonspatial symmetries in all spatial dimensions (the ‘tenfold way'), which differs from its equilibrium counterpart. Direct physical consequences of our classification are discussed, including important ramifications for the use of topological zero-energy bound states in quantum information technologies.

The Lieb-Schultz-Mattis (LSM) theorem and its higher-dimensional generalizations by Oshikawa and Hastings establish that a translation-invariant lattice model of spin-${\frac{1}{2}}^{\prime }\mathrm{s}$ can not have a nondegenerate ground state preserving both spin and translation symmetries. Recently, it was shown that LSM theorems can be interpreted in terms of bulk-boundary correspondence of certain weak symmetry-protected topological (SPT) phases. In this work, we discuss LSM-type theorems for two-dimensional fermionic systems, which have no bosonic analogs. They follow from a general classification of weak SPT phases of fermions in three dimensions. We further derive constraints on possible gapped symmetry-enriched topological phases in such systems. In particular, we show that lattice translations must permute anyons, thus leading to “symmetry-enforced” non-Abelian dislocations, or “genons.” We also discuss surface states of other weak SPT phases of fermions.

In 1915, Einstein and de Haas and Barnett demonstrated that changing the magnetization of a magnetic material results in mechanical rotation and vice versa. At the microscopic level, this effect governs the transfer between electron spin and orbital angular momentum, and lattice degrees of freedom, understanding which is key for molecular magnets, nano-magneto-mechanics, spintronics, and ultrafast magnetism. Until now, the timescales of electron-to-lattice angular momentum transfer remain unclear, since modeling this process on a microscopic level requires the addition of an infinite amount of quantum angular momenta. We show that this problem can be solved by reformulating it in terms of the recently discovered angulon quasiparticles, which results in a rotationally invariant quantum many-body theory. In particular, we demonstrate that nonperturbative effects take place even if the electron-phonon coupling is weak and give rise to angular momentum transfer on femtosecond timescales.

We develop a folding approach to study two-dimensional symmetry-enriched topological (SET) phases with the mirror reflection symmetry. Our folding approach significantly transforms the mirror SETs, such that their properties can be conveniently studied through previously known tools: (i) it maps the nonlocal mirror symmetry to an onsite ${\mathbb{Z}}_2$ layer-exchange symmetry after folding the SET along the mirror axis, so that we can gauge the symmetry; (ii) it maps all mirror SET information into the boundary properties of the folded system, so that they can be studied by the anyon condensation theory—a general theory for studying gapped boundaries of topological orders; and (iii) it makes the mirror anomalies explicitly exposed in the boundary properties, i.e., strictly 2D SETs and those that can only live on the surface of a 3D system can be easily distinguished through the folding approach. With the folding approach, we derive a set of physical constraints on data that describes mirror SET, namely, mirror permutation and mirror symmetry fractionalization on the anyon excitations in the topological order. We conjecture that these constraints may be complete, in the sense that all solutions are realizable in physical systems. Several examples are discussed to justify this. Previously known general results on the classification and anomalies are also reproduced through our approach.

We investigate topological Cooper pairing, including gapless Weyl and fully gapped class DIII superconductivity, in a three-dimensional doped Luttinger semimetal. The latter describes effective spin-3/2 carriers near a quadratic band touching and captures the normal-state properties of the 227 pyrochlore iridates and half-Heusler alloys. Electron-electron interactions may favor non-$s$-wave pairing in such systems, including even-parity $d$-wave pairing. We argue that the lowest energy $d$-wave pairings are always of complex (e.g., $d+id$) type, with nodal Weyl quasiparticles. This implies $\varrho \left(E\right)\sim {\left|E\right|}^2$ scaling of the density of states (DoS) at low energies in the clean limit or $\varrho \left(E\right)\sim \left|E\right|$ over a wide critical region in the presence of disorder. The latter is consistent with the $T$ dependence of the penetration depth in the half-Heusler compound YPtBi. We enumerate routes for experimental verification, including specific heat, thermal conductivity, NMR relaxation time, and topological Fermi arcs. Nucleation of any $d$-wave pairing also causes a small lattice distortion and induces an $s$-wave component; this gives a route to strain-engineer exotic $s+d$ pairings. We also consider odd-parity, fully gapped $p$-wave superconductivity. For hole doping, a gapless Majorana fluid with cubic dispersion appears at the surface. We invent a generalized surface model with $\nu$-fold dispersion to simulate a bulk with winding number $\nu$. Using exact diagonalization, we show that disorder drives the surface into a critically delocalized phase, with universal DoS and multifractal scaling consistent with the conformal field theory (CFT) SO($n){}_{\nu }$, where $n\to 0$ counts replicas. This is contrary to the naive expectation of a surface thermal metal, and implies that the topology tunes the surface renormalization group to the CFT in the presence of disorder.

We report on nonequilibrium properties of graphene probed by superconducting tunnel spectroscopy. A hexagonal boron nitride (hBN) tunnel barrier in combination with a superconducting Pb contact is used to extract the local energy distribution function of the quasiparticles in graphene samples in different transport regimes. In the cases where the energy distribution function resembles a Fermi-Dirac distribution, the local electron temperature can directly be accessed. This allows us to study the cooling mechanisms of hot electrons in graphene. In the case of long samples (device length $L$ much larger than the electron-phonon scattering length $l_{\text{e-ph}}$), cooling through acoustic phonons is dominant. We find a crossover from the dirty limit with a power law $T^3$ at low temperature to the clean limit at higher temperatures with a power law $T^4$ and a deformation potential of 13.3 eV. For shorter samples, where $L$ is smaller than $l_{\text{e-ph}}$ but larger than the electron-electron scattering length $l_{\text{e-e}}$, the well-known cooling through electron out-diffusion is found. Interestingly, we find strong indications of an enhanced Lorenz number in graphene. We also find evidence of a non-Fermi-Dirac distribution function, which is a result of noninteracting quasiparticles in very short samples.

Topology and electron interactions are two central themes in modern condensed matter physics. Here, we propose graphene-based systems where both the band topology and interaction effects can be simply controlled with electric fields. We study a number of systems of twisted double layers with small twist angle where a moiré superlattice is formed. Each layer is chosen to be either AB-stacked bilayer graphene, ABC-stacked trilayer graphene, or hexagonal boron nitride. In these systems, a vertical applied electric field enables control of the bandwidth, and interestingly also the Chern number. We find that the Chern numbers of the bands associated with each of the two microscopic valleys can be $\pm 0,\pm 1,\pm 2,\pm 3$ depending on the specific system and vertical electrical field. We show that these graphene moiré superlattices are promising platforms to realize a number of fascinating many-body phenomena, including (fractional) quantum anomalous Hall effects. We also discuss conceptual similarities and implications for modeling twisted bilayer graphene systems.

The search of unconventional magnetic and nonmagnetic states is a major topic in the study of frustrated magnetism. Canonical examples of those states include various spin liquids and spin nematics. However, discerning their existence and the correct characterization is usually challenging. Here we introduce a machine-learning protocol that can identify general nematic order and their order parameter from seemingly featureless spin configurations, thus providing comprehensive insight on the presence or absence of hidden orders. We demonstrate the capabilities of our method by extracting the analytical form of nematic order parameter tensors up to rank 6. This may prove useful in the search for novel spin states and for ruling out spurious spin liquid candidates.

We use angle-resolved photoemission spectroscopy with a 7-eV laser, which is capable of ultrahigh energy and momentum resolutions, and investigate bosonic mode couplings in the surface bands of ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$. Significantly, our measurements reveal pronounced kink structures at very low binding energies ($\sim 8$ and $\sim 15$ meV), which have a strong variation in the renormalization strength among multiple bands derived from the $\mathrm{Ru}4d$ orbitals. Neutron scattering has observed phonon modes with the lowest energy scale around 15 meV, which thus could be the main source for the $\sim 15$-meV kink. In contrast, the significant coupling at the lower energy ($\sim 8$ meV) is attributed to magnetic excitations, which are reported to be peaked in density of states around 10 meV. The $\sim 8$-meV kink is found to be strongest in the two-dimensional $4d_{xy}$-derived band, implying its mechanism to be the electron coupling to ferromagnetic spin fluctuations.

We study the effect of photonic spin-orbit coupling (SOC) in micropillar lattices on the topological edge states of a one-dimensional chain with a zigzag geometry, corresponding to the Su-Schrieffer-Heeger model equipped with an additional internal degree of freedom. The system combines the strong hopping anisotropy of the $p$-type pillar modes with the large TE-TM splitting in Bragg microcavities. By resolving the photoluminescence emission in energy and polarization we probe the effects of the resulting SOC on the spatial and spectral properties of the edge modes. We find that the edge modes feature a fine structure of states that penetrate by different amounts into the bulk of the chain, depending on the strength of the SOC terms present, thereby opening a route to manipulation of the topological states in the system.

Anticipating the low-energy arrangements of atoms in space is an indispensable scientific task. Modern stochastic approaches to searching for these configurations depend on the optimization of structures to nearby local minima in the energy landscape. In many cases these local minima are relatively high in energy, and inspection reveals that they are trapped, tangled, or otherwise frustrated in their descent to a lower-energy configuration. Strategies have been developed which attempt to overcome these traps, such as classical and quantum annealing, basin/minima hopping, evolutionary algorithms, and swarm-based methods. Random structure search makes no attempt to avoid the local minima and benefits from a broad and uncorrelated sampling of configuration space. It has been particularly successful in the first-principles prediction of unexpected new phases of dense matter. Here it is demonstrated that by starting the structural optimizations in a higher-dimensional space, or hyperspace, many of the traps can be avoided and that the probability of reaching low-energy configurations is much enhanced. Excursions into the extra dimensions are progressively eliminated through the application of a growing energetic penalty. This approach is tested on hard cases for random search: clusters, compounds, and covalently bonded networks. The improvements observed are most dramatic for the most difficult ones. Random structure search is shown to be typically accelerated by two orders of magnitude and more for particularly challenging systems. This increase in performance is expected to benefit all approaches to structure prediction that rely on the local optimization of stochastically generated structures.

We propose to realize the pseudo-Hermiticity in a cavity magnonics system consisting of the Kittel modes in two small yttrium iron garnet spheres coupled to a microwave cavity mode. The effective gain of the cavity can be achieved using the coherent perfect absorption of the two input fields fed into the cavity. With certain constraints of the parameters, the Hamiltonian of the system has pseudo-Hermiticity, and its eigenvalues can be either all real or one real and other two constituting a complex-conjugate pair. By varying the coupling strengths between the two Kittel modes and the cavity mode, we find the existence of the third-order exceptional point in the parameter space in addition to the usual second-order exceptional point existing in the system with parity-time symmetry. Also, we show that these exceptional points can be demonstrated by measuring the output spectrum of the cavity.

We report a spectral ellipsometry study of multilayers composed of superconducting $\mathrm{YB}{\mathrm{a}}_2\mathrm{C}{\mathrm{u}}_3{\mathrm{O}}_{6+\delta }$ (YBCO) and ferromagnetic $\mathrm{L}{\mathrm{a}}_{0.7}\mathrm{C}{\mathrm{a}}_{0.3}\mathrm{Mn}{\mathrm{O}}_3$ (LCMO) in the spectral range 0.7–6.5 eV. With increasing YBCO sublayer thickness, the optical spectral weight is enhanced at photon energies of 1.5–3.5 eV. The spectral weight enhancement is proportional to the number of interfaces of each multilayer sample, indicating its association with the interfacial electronic structure. Based on calculations in the framework of a multilayer model, we find that the shape of the interface-induced spectral weight is consistent with transfer of hole carriers from YBCO to LCMO. Our results imply that the holes that are transferred across the interfaces accumulate in the LCMO layers, rather than being pinned by interfacial defects or annihilated by electron donors such as oxygen vacancies. Optical spectroscopy can thus serve as a nondestructive probe of charge transfer across buried interfaces in metal-oxide heterostructures.

We construct a two-parametric family of integrable models and reveal their underlying duality symmetry. A modular subgroup of this duality is shown to connect noninteracting modes of different models. We apply this solution and duality to a Richardson-Gaudin model and generate a novel integrable system termed the $s\text{−}d$ wave Richardson-Gaudin-Kitaev interacting chain, interpolating $s$- and $d$-wave superconductivity. The phase diagram of this interacting model has a topological phase transition that can be connected to the duality, where the occupancy of the noninteracting mode serves as a topological order parameter.

We consider the effects of the electron-electron interaction in a clean Dirac metal, i.e., a Dirac system with the chemical potential not tuned to the Dirac point. We introduce the notion of a Dirac-Fermi liquid (DFL) and discuss the soft two-particle excitations in such systems, which are qualitatively different from the corresponding excitations in a conventional, or Landau-Fermi liquid (LFL). These soft excitations lead to nonanalytic dependencies of observables, including the density of states, the spin susceptibility, and the specific heat, on the temperature, magnetic field, and wave number, which first appear at second order in the interaction. We determine and discuss the nature of these nonanalyticities in a DFL and compare them with the corresponding effects in a LFL. Our results are based on very general arguments regarding the existence and nature of the soft modes, and corroborated by explicit perturbative calculations. We also discuss their consequences for magnetic quantum phase transitions in Dirac metals.

Within the framework of density functional perturbation theory, we implement and test a “metric wave” response-function approach. It consists in the reformulation of an acoustic phonon perturbation in the curvilinear frame that is comoving with the atoms. This means that all the perturbation effects are encoded in the first-order variation of the real-space metric, while the atomic positions remain fixed. This approach can be regarded as the generalization of the uniform strain perturbation of Hamann et al. [D. R. Hamann, X. Wu, K. M. Rabe, and D. Vanderbilt, Phys. Rev. B 71, 035117 (2005)] to the case of inhomogeneous deformations, and greatly facilitates the calculation of advanced electromechanical couplings such as the flexoelectric tensor. We demonstrate the accuracy of our approach with extensive tests on model systems and on bulk crystals of Si and ${\mathrm{SrTiO}}_3$.

Coulomb bound electron-hole pairs, excitons, govern the optical properties of semiconducting transition-metal dichalcogenides like ${\mathrm{MoS}}_2$ and ${\mathrm{WSe}}_2$. We study optical transitions at the $K$ point for $2H$ homobilayer ${\mathrm{MoS}}_2$ in density functional theory including excitonic effects and compare them with reflectivity measurements in high-quality samples encapsulated in hexagonal BN. In both calculated and measured spectra we find a strong interlayer exciton transition in energy between A and B intralayer excitons, observable for $T=4–300$ K, whereas no such transition is observed for the monolayer in the same structure in this energy range. The interlayer excitons consist of an electron localized in one layer and a hole state delocalized over the bilayer, which results in the unusual combination of high oscillator strength and a static dipole moment. We also find signatures of interlayer excitons involving the second-highest valence band (B) and compare absorption calculations for different bilayer stackings. For homotrilayer ${\mathrm{MoS}}_2$ we also observe interlayer excitons and an energy splitting between different intralayer A excitons originating from the middle and outer layers, respectively.

Floquet engineering offers tantalizing opportunities for controlling the dynamics of quantum many-body systems and realizing new nonequilibrium phases of matter. However, this approach faces a major challenge: generic interacting Floquet systems absorb energy from the drive, leading to uncontrolled heating which washes away the sought-after behavior. How to achieve and control a nontrivial nonequilibrium steady state is therefore of crucial importance. In this work, we study the dynamics of an interacting one-dimensional periodically driven electronic system coupled to a phonon heat bath. Using the Floquet-Boltzmann equation (FBE) we show that the electronic populations of the Floquet eigenstates can be controlled by the dissipation. We find the regime in which the steady state features an insulator-like filling of the Floquet bands, with a low density of additional excitations. Furthermore, we develop a simple rate equation model for the steady state excitation density that captures the behavior obtained from the numerical solution of the FBE over a wide range of parameters.