We present a stochastic algorithm for constructing a topologically disordered (i.e., nonregular) spatial lattice with nodes of constant coordination number, the CC lattice. The construction procedure dramatically improves on an earlier proposal [Schrauth, Richter, and Portela, Phys. Rev. E 97, 022144 (2018)] with respect to both computational complexity and finite-size scaling properties—making the CC lattice an alternative to proximity graphs which, especially in higher dimensions, is significantly faster to build. Among other applications, physical systems such as certain amorphous materials with low concentration of coordination defects are an important example of disordered, constant-coordination lattices in nature. As a concrete application, we characterize the criticality of the 3D Ising model on the CC lattice. We find that its phase transition belongs to the clean Ising universality class, establishing that the disorder present in the CC lattice is a nonrelevant perturbation for this model in the sense of renormalization group theory.

The dynamic structure factor of materials is proportional to their linear electronic response and it displays their excitation spectra. Usually the response is measured on the same length scale as the perturbation. Here, we illustrate that much can be gained by studying also the mixed dynamic structure factor, which connects different spatial components of perturbation and response. We extend state-of-the-art ab initio calculations to access the mixed dynamic structure factor, including excitonic effects. Using bulk silicon and lithium fluoride as prototype examples, we show that these effects play a crucial role above and below the quasiparticle gap, and are needed in order to explain coherent inelastic x-ray scattering experiments. Our approach also yields important information concerning the microscopic structure of time-dependent density functional theory.

By measuring the Josephson emission of a diffusive superconductor–normal metal–superconductor (SNS) junction we access the harmonic content of the current-phase relation (CPR). We experimentally identify a nonadiabatic regime in which the CPR is modified by high frequency microwave irradiation. This observation is explained by the excitation of quasiparticles in the normal wire induced by the electromagnetic field. The distortion of the CPR originates from the phase-dependent out-of-equilibrium distribution function which is strongly affected by the ac response of the spectral supercurrent. For a phase difference approaching $\pi$, transitions across the minigap are dynamically favored, leading to a supercurrent reduction. This finding is supported by a comparison with the quasiclassical Green's function theory of superconductivity in diffusive SNS junctions under microwave irradiation.

Achieving atomically flat and stoichiometric films of complex multicomponent oxides is crucial to integrating these materials in both established and emerging technologies. While pulsed laser deposition (PLD) can in principle produce these high-quality films, growth experiments often result in unsatisfactory morphologies with rough surfaces and nonstoichiometric compositions. To understand the cause, the growth needs to be followed at an atomic level from its early stages as a function of the growth conditions. By combining PLD with atomically resolved scanning tunneling microscopy, as well as surface spectroscopic and diffraction techniques, we address the origin of surface roughening in ${\text{SrTiO}}_3$(110) homoepitaxial films and pinpoint optimal growth conditions. We highlight the importance of surface reconstructions at all stages of growth: The different sticking on coexisting surface structures is responsible for the roughening of ${\text{SrTiO}}_3$(110) films and affects their stoichiometry.

A many-particle system must possess long-range interactions in order to be hyperuniform at thermal equilibrium. Hydrodynamic arguments and numerical simulations show, nevertheless, that a three-dimensional elastic-line array with short-ranged repulsive interactions, such as vortex matter in a type-II superconductor, forms at equilibrium a class-II hyperuniform two-dimensional point pattern for any constant-$z$ cross section. In this case, density fluctuations vanish isotropically as $\sim q^{\alpha }$ at small wave vectors $q$, with $\alpha =1$. This prediction includes the solid and liquid vortex phases in the ideal clean case and the liquid in presence of weak uncorrelated disorder. We also show that the three-dimensional Bragg glass phase is marginally hyperuniform, while the Bose glass and the liquid phase with correlated disorder are expected to be nonhyperuniform at equilibrium. Furthermore, we compare these predictions with experimental results on the large-wavelength vortex density fluctuations of magnetically decorated vortex structures nucleated in pristine, electron-irradiated, and heavy-ion-irradiated superconducting ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ samples in the mixed state. For most cases, we find hyperuniform two-dimensional point patterns at the superconductor surface with an effective exponent ${\alpha }_{\text{eff}}\approx 1$. We interpret these results in terms of a large-scale memory of the high-temperature line-liquid phase retained in the glassy dynamics when field cooling the vortex structures into the solid phase. We also discuss the crossovers expected from the dispersivity of the elastic constants at intermediate length-scales, and the lack of hyperuniformity in the $x\text{−}y$ plane for lengths $q^{-1}$ larger than the sample thickness due to finite-size effects in the $z$ direction. We argue these predictions may be observable and propose further imaging experiments to test them independently.

Recently, it was realized that anomalies can be completely classified by topological orders, symmetry protected topological orders, and symmetry enriched topological orders in one higher dimension. The anomalies that people used to study are invertible anomalies that correspond to invertible topological orders and/or symmetry protected topological orders in one higher dimension. In this paper, we introduce a notion of noninvertible anomaly, which describes the boundary of generic topological order. It is characterized by two features. First, a theory with noninvertible anomaly has a multicomponent partition function. Second, under the mapping class group transformation of space-time, the vector of partition functions transform covariantly. In fact, the anomalous partition functions transform in the same way as the degenerate ground states of the corresponding topological order in one higher dimension. This general theory of noninvertible anomaly may have wide applications. As an example, we show that the irreducible gapless boundary of 2+1D double-semion topological order must have central charge $c=\overline{c}>\frac{25}{28}$.

We show that in a generic, ergodic quantum many-body system the interactions induce a nontrivial topology for an arbitrarily small non-Hermitian component of the Hamiltonian. This is due to an exponential-in-system-size proliferation of exceptional points which have the Hermitian limit as an accumulation (hyper)surface. The nearest-neighbor level repulsion characterizing Hermitian ergodic many-body systems is thus shown to be a projection of a richer phenomenology, where actually all the exponentially many eigenvalues are pairwise connected in a topologically robust fashion via exceptional points.

It is known that, under the presence of a static external magnetic field $B_e$, an electromagnetic field rotates its polarization axes (Faraday rotation) when transmitted across a graphene single layer. Graphene provides record values of Faraday angle per layer thickness, but at frequencies of the order of the cyclotron frequency. This impedes applications, as fields of the order of 10 T would be required even for terahertz operation. Here we show that this condition is relaxed in strained graphene, where the potentially large induced pseudomagnetic field $B_{\text{ps}}$, when combined with a small $B_e$ (needed to break time-reversal symmetry), provides large Faraday rotation at arbitrary frequencies. It is found that the Faraday rotation in this system presents a very rich dependence on all different parameters, being greatly enhanced when the number of occupied Landau levels (governed by $B_e\pm B_{\text{ps}}$) is different in the two graphene valleys.

We observe a set of three replica luminescent peaks at ∼21.4 meV below the dark exciton, and negative and positive dark trions (or exciton polarons) in monolayer $\mathrm{WS}{\mathrm{e}}_2$. The replica redshift energy matches the energy of the zone-center $E^{\prime \prime }$-mode optical phonons. The phonon replicas exhibit a parallel gate dependence and the same $g$-factors as the dark excitonic states, but follow the valley selection rules of the bright excitonic states. While the dark states exhibit an out-of-plane transition dipole and valley-independent linearly polarized emission in the in-plane directions, their phonon replicas exhibit an in-plane transition dipole and valley-dependent circularly polarized emission in the out-of-plane directions. Our results and symmetry analysis show that the $K$-valley dark exciton decays into a left-handed chiral phonon and a right-handed photon, whereas the $K^{\prime }$-valley dark exciton decays into a right-handed chiral phonon and a left-handed photon. Such valley selection rules of chiral phonon replicas can be utilized to identify the valleys of the dark excitonic states and explore their chiral interactions with phonons.

The information convex allows us to look into certain information-theoretic constraints in two-dimensional topological orders. We provide a derivation of the topological contribution $ln{d}_a$ to the von Neumann entropy, where $d_a$ is the quantum dimension of anyon $a$. This value emerges as the only value consistent with strong subadditivity, assuming a certain topological dependence of the information convex structure. In particular, it is assumed that the fusion multiplicities are coherently encoded in a two-hole disk. A similar contribution ($ln{d}_{\alpha }$) is derived for gapped boundaries. This method further allows us to identify the fusion probabilities and certain constraints on the fusion theory. We also derive a linear bound on the circuit depth of unitary non-Abelian string operators and discuss how it generalizes and changes in the presence of a gapped boundary.

The thermodynamic properties of the Shastry-Sutherland model have posed one of the longest-lasting conundrums in frustrated quantum magnetism. Over a wide range on both sides of the quantum phase transition (QPT) from the dimer-product state to the plaquette-based ground state, neither analytical nor any available numerical methods have come close to reproducing the physics of the excited states and thermal response. We solve this problem in the dimer-product phase by introducing two qualitative advances in computational physics. One is the use of thermal pure quantum (TPQ) states to augment dramatically the size of clusters amenable to exact diagonalization. The second is the use of tensor-network methods, in the form of infinite projected entangled-pair states (iPEPS), for the calculation of finite-temperature quantities. We demonstrate convergence as a function of system size in TPQ calculations and of bond dimension in our iPEPS results, with complete mutual agreement even extremely close to the QPT. Our methods reveal a remarkably sharp and low-lying feature in the magnetic specific heat, whose origin appears to lie in a proliferation of excitations composed of two-triplon bound states. The surprisingly low energy scale and apparently extended spatial nature of these states explain the failure of less refined numerical approaches to capture their physics. Both of our methods will have broad and immediate application in addressing the thermodynamic response of a wide range of highly frustrated magnetic models and materials.

Motivated by recent advances in the fabrication of Josephson junctions in which the weak link is made of a low-dimensional nonsuperconducting material, we present here a systematic theoretical study of the local density of states (LDOS) in a clean two-dimensional normal metal (N) coupled to two $s$-wave superconductors (S). To be precise, we employ the quasiclassical theory of superconductivity in the clean limit, based on Eilenberger's equations, to investigate the phase-dependent LDOS as a function of factors such as the length or the width of the junction, a finite reflectivity, and a weak magnetic field. We show how the spectrum of Andreev bound states that appear inside the gap shape the phase-dependent LDOS in short and long junctions. We discuss the circumstances when a gap appears in the LDOS and when the continuum displays a significant phase dependence. The presence of a magnetic flux leads to a complex interference behavior, which is also reflected in the supercurrent-phase relation. Our results agree qualitatively with recent experiments on graphene SNS junctions. Finally, we show how the LDOS is connected to the supercurrent that can flow in these superconducting heterostructures and present an analytical relation between these two basic quantities.

We construct an exactly solvable lattice model of a fractional Weyl semimetal. The low-energy theory of this strongly interacting state is that of a Weyl semimetal built out of fractionally charged fermions. We show the existence of a universally quantized and fractional circular photogalvanic effect and a violation of the Wiedemann-Franz law in the system. Together with a spectral gap in the single-particle electronic Green's function, they provide strong experimental signatures for this exotic gapless state of matter.

A closed-trajectory evolution of a quantum state generally imprints a phase that contains both dynamical and geometrical contributions. While dynamical phases depend on the reference system, geometric phase factors are uniquely defined by the properties of the outlined trajectory. Here we generate and measure geometric phases in a Bose-Einstein condensate of ${}^{87}\mathrm{Rb}$ using a combination of the dynamical quantum Zeno effect and measurement-free evolution. We show that the dynamical quantum Zeno effect can inhibit the formation of a geometric phase without altering the dynamical phase. This can be used to extract the geometric Aharonov-Anandan phase from any closed-trajectory evolution without requiring knowledge or control of the Hamiltonian.

The degree of nonorthogonality of eigenstates of non-Hermitian systems governs nuclear scattering, electronic conductance, and wave propagation in disordered media. Here, we determine the impact of non-Hermiticity upon eigenstates inside an open random cavity from measurements of the modal overlap matrix of transmitted microwave radiation. Increasing eigenfunction correlation with spectral modal overlap brought about by the openness of the system leads to modal transmission greatly exceeding unity accompanied by strong modal anticorrelation guaranteeing that transmission does not exceed unity.

We show how the universal low-energy properties of Weyl semimetals with spatially varying time-reversal (TR) or inversion (I) symmetry breaking are described in terms of chiral fermions experiencing curved-spacetime geometry and synthetic gauge fields. By employing Clifford representations and Schrieffer-Wolff transformations, we present a systematic derivation of an effective curved-space Weyl theory with rich geometric and gauge structure. To illustrate the utility of the formalism, we give a concrete prescription of how to fabricate nontrivial curved spacetimes and event horizons in topological insulators with magnetic textures. Our theory can also account for strain-induced effects, providing a powerful unified framework for studying and designing inhomogeneous Weyl materials.

We investigate the electronic structure of a recently discovered, heavily electron-doped iron-based superconductor ${\mathrm{LaFe}}_2{\mathrm{As}}_2$. Although first-principles calculation shows apparent absence of hole Fermi surfaces around the $\mathrm{\Gamma }$ point, we reveal, by hypothetically removing the La $d$ orbital contribution, that a hole Fermi surface around the $\mathrm{\Gamma }$ point is essentially present. In the collapsed phase of ${\mathrm{LaFe}}_2{\mathrm{As}}_2$, which is nonsuperconducting, the hole Fermi surface is found to be absent, and the difference from the uncollapsed superconducting phase can be naturally understood within the spin-fluctuation-mediated pairing scenario.

In recent years, there have been rapid advances in the parallel fields of electronic and photonic topological crystals. Topological photonic crystals in particular show promise for coherent transport of light and quantum information at macroscopic scales. In this work, we apply for the first time the recently developed theory of “topological quantum chemistry” to the study of band structures in photonic crystals. This method allows us to design and diagnose topological photonic band structures using only group theory and linear algebra. As an example, we focus on a family of crystals formed by elliptical rods in a triangular lattice. We show that the symmetry of Bloch states in the Brillouin zone can determine the position of the localized photonic wave packets describing groups of bands. By modifying the crystal structure and inverting bands, we show how the centers of these wave packets can be moved between different positions in the unit cell. Finally, we show that for shapes of dielectric rods, there exist isolated topological bands which do not admit a well-localized description, representing the first physical instance of “fragile” topology in a truly noninteracting system. Our work demonstrates how photonic crystals are the natural platform for the future experimental investigation of fragile topological bands.

The precise determination of the excitation energies in condensed-phase molecular systems is important for understanding system-environment interactions as well as for the prerequisite input data of theoretical models used to study the dynamics of the system. The excitation energies are usually determined by fitting of the measured optical spectra that contain broad and unresolved peaks as a result of the thermally random dynamics of the environment. Herein, we propose a method for precise energy determination by strongly coupling the molecular system to an optical cavity and measuring the energy of the resulting polariton. The effect of thermal fluctuations induced by the environment on the polariton is also investigated, from which a power scaling law relating the polariton's linewidth to the number of molecules is obtained. The power exponent gives important information about the environmental dynamics.

A theoretical framework is developed that permits construction of biskyrmion lattices observed in nonchiral magnetic films. Skyrmion and antiskyrmion configurations are discussed. We study films of finite thickness containing up to $1000\times 1000\times 100$ spins. Hexatic biskyrmion lattices in a pure two-dimensional (2D) exchange model are naturally described by the Weierstrass  $\wp$  and $\zeta$ elliptic functions. Starting with such a lattice as an initial state, we investigate how it evolves toward a minimum-energy state in a zero magnetic field in the presence of perpendicular magnetic anisotropy (PMA) and dipole-dipole interaction. Metastable biskyrmion lattices exist at low PMA. At higher PMA, we observe stable triangular lattices of biskyrmion bubbles containing Bloch lines, whose energies are lower than the energy of the uniformly magnetized state.