The standard models contain chiral fermions coupled to gauge theories. It has been a longstanding problem to give such gauged chiral fermion theories a quantum nonperturbative definition. By classification of quantum anomalies (including perturbative local anomalies and nonperturbative global anomalies) and symmetric interacting invertible topological orders via a mathematical cobordism theorem for differentiable and triangulable manifolds, and by the existence of a symmetric gapped boundary (designed for the mirror sector) on the trivial symmetric invertible topological orders, we propose that Spin(10) chiral fermion theories with Weyl fermions in 16-dimensional spinor representations can be defined on a $3+1\mathrm{D}$ lattice without fermion doubling, and subsequently dynamically gauged to be a Spin(10) chiral gauge theory. As a result, the standard models from the $16n$-chiral fermion SO(10) grand unification can be defined nonperturbatively via a $3+1\mathrm{D}$ local lattice model of bosons or qubits. Furthermore, we propose that standard models from the $15n$-chiral fermion SU(5) Grand Unification can be regularized by a $3+1\mathrm{D}$ local lattice model of fermions.

We study analytically and numerically dynamics and eigenstates of two electrons with Coulomb repulsion on a tight-binding lattice in one and two dimensions. The total energy and momentum of electrons are conserved and we show that for a certain momentum range the dynamics is exactly reduced to an evolution in an effective narrow energy band where the energy conservation forces the two electrons to propagate together through the whole system at moderate or even weak repulsion strength. We argue that such a mechanism of electron pair formation by the repulsive Coulomb interaction is rather generic and that it can be at the origin of unconventional superconductivity in twisted bilayer graphene.

We discuss a new class of quantum phase transitions—deconfined Mott transition (DMT)—that describe a continuous transition between a Fermi liquid metal with a generic electronic Fermi surface and an electrical insulator without Fermi surfaces of emergent neutral excitations. We construct a unified $U\left(2\right)$ gauge theory to describe a variety of metallic and insulating phases, which include Fermi liquids, fractionalized Fermi liquids (FL*), conventional insulators, and quantum spin liquids, as well as the quantum phase transitions between them. Using the DMT as a basic building block, we propose a distinct quantum phase transition—deconfined metal-metal transition (${\mathrm{DM}}^2\mathrm{T}$)—that describes a continuous transition between two metallic phases, accompanied by a jump in the size of their electronic Fermi surfaces (also dubbed a ‘Fermi transition'). We study these new classes of deconfined metallic quantum critical points using a renormalization group framework at the leading nontrivial order in a controlled expansion and comment on the various interesting scenarios that can emerge going beyond this leading order calculation. We also study a $U\left(1\right)\times U\left(1\right)$ gauge theory that shares a number of similarities with the $U\left(2\right)$ gauge theory and sheds important light on many phenomena related to DMT, ${\mathrm{DM}}^2\mathrm{T}$, and quantum spin liquids.

Synchrotron x-ray-diffraction measurements on single crystals of the double perovskite $\mathrm{B}{\mathrm{a}}_2\mathrm{MgRe}{\mathrm{O}}_6$ with $5d^1$ electronic configurations reveal the successive phase transitions from a disordered state to a quadrupolar order at $T_q=33\mathrm{K}$, and then, to a dipolar ordered state at $T_m=18\mathrm{K}$. The magnetic reflections observed below $T_m$ are indexed to a propagation vector with $k=\left[001\right]$, indicating a canted antiferromagnetic order. The very small deformation of $\mathrm{Re}{\mathrm{O}}_6$ octahedra observed below $T_q$ demonstrates that the quadrupolar order is composed of antiferroically arranged $Q_{x^2\text{–}{y}^2}$ and ferroically arranged $Q_{3z^2\text{–}{r}^2}$ moments. These observations are consistent with the mean-field theory for spin-orbit-entangled electrons. Our findings are a significant step towards understanding the intriguing physics of multipoles realized by spin-orbit-entangled $5d$ electrons.

We analyze the impacts of crystalline symmetry on non-Hermitian skin effects. Focusing on mirror symmetry, we propose another type of skin effect, a mirror skin effect, which results in a significant dependence of the energy spectrum on the boundary condition only for the mirror invariant line in the two-dimensional Brillouin zone. This effect arises from the topological properties characterized by a mirror winding number. We further reveal that the mirror skin effect can be observed for an electric circuit composed of negative impedance converters with a current inversion where switching the boundary condition significantly changes the admittance eigenvalues only along the mirror invariant lines. Furthermore, we demonstrate that extensive localization of the eigenstates for each mirror sector results in an anomalous voltage response.

We study the dynamics of Dirac and Weyl electrons in disordered point-node semimetals. The ballistic feature of the transport is demonstrated by simulating the wave-packet dynamics on lattice models. We show that the ballistic transport survives under a considerable strength of disorder up to the semimetal-metal transition point, which indicates the robustness of point-node semimetals against disorder. We also visualize the robustness of the nodal points and linear dispersion under broken translational symmetry. The speed of the wave packets slows down with increasing disorder strength, and vanishes toward the critical strength of disorder, hence becoming the order parameter. The obtained critical behavior of the speed of the wave packets is consistent with that predicted by the scaling conjecture.

Symmetry is at the heart of modern physics. Phases of matter are classified by symmetry breaking, topological phases are characterized by nonlocal symmetries, and point group symmetries are critical to our understanding of crystalline materials. Symmetries could then be used as a criterion to engineer quantum systems with targeted properties. Toward that end, we have developed an approach, the symmetric Hamiltonian construction (SHC), that takes as input symmetries, specified by integrals of motion or discrete symmetry transformations, and produces as output all local Hamiltonians consistent with these symmetries. This approach builds on the slow operator method [H. Kim, M. C. Bañuls, J. I. Cirac, M. B. Hastings, and D. A. Huse, Phys. Rev. E 92, 012128 (2015)]. We use our new approach to construct new Hamiltonians for topological phases of matter. Topological phases of matter are exotic quantum phases with potential applications in quantum computation. In this work, we focus on two types of topological phases of matter: superconductors with Majorana zero modes and $Z_2$ quantum spin liquids. In our first application of the SHC approach, we analytically construct a large and highly tunable class of superconducting Hamiltonians with Majorana zero modes with a given targeted spatial distribution. This result lays the foundation for potential new experimental routes to realizing Majorana fermions. In our second application, we find new $Z_2$ spin-liquid Hamiltonians on the square and Kagome lattices. These new Hamiltonians are not sums of commuting operators nor frustration free and, when perturbed appropriately (in a way that preserves their $Z_2$ spin-liquid behavior), exhibit level-spacing statistics that suggest nonintegrability. This result demonstrates how our approach can automatically generate new spin-liquid Hamiltonians with interesting properties not often seen in solvable models.

Bound states at interfaces between superconductors and other materials are a powerful tool to characterize the nature of the involved systems and to engineer elusive quantum excitations. In-gap excitations of conventional $s$-wave superconductors occur, for instance, at magnetic impurities with net magnetic moment breaking time-reversal symmetry. Here we show that interfaces between a superconductor and a quantum antiferromagnet can host robust in-gap excitations, without breaking time-reversal symmetry. We illustrate this phenomenon in a one-dimensional model system with an interface between a conventional $s$-wave superconductor and a one-dimensional Mott insulator described by a standard Hubbard model. This genuine many-body problem is solved exactly by employing a combination of kernel polynomial and tensor network techniques. We unveil the nature of such zero modes by showing that they can be adiabatically connected to solitonic solutions between a superconductor and a mean-field antiferromagnet. Our results put forward a new class of in-gap excitations between superconductors and a disordered quantum spin phase, including quantum spin-liquids, that can be relevant for a wider range of heterostructures.

We investigate the gyrotropic birefringence (GB) that is a light-propagation-direction-dependent nonreciprocal response of birefringence, arising from the dynamical magnetoelectric coupling in a multiferroic manganite with spin-cycloid order in terms of time-domain terahertz polarimetry. The GB shows up as the enhanced nonreciprocal optical rotation on electromagnon resonance. The magnitude of the GB is found to scale with the bilinear coupling of ferroic order parameters $P·M$ ($P$: electric polarization, $M$: magnetization) through the magnetic-field dependence with spin-flop transition. Quantitative spectral analysis reveals that the intermode coupling of electromagnon and antiferromagneic resonance plays an essential role for the enhancement of the GB.

We observe and characterize two nonlinear light-amplification regimes with unique spectral properties and fluence dependencies in laser-excited fused silica using ultrafast pump-probe imaging spectroscopy. The two underlying mechanisms are switchable within 150 fs via the time delay between an intense near-infrared femtosecond pump and an ultraviolet femtosecond probe pulse. While the earlier amplification regime is linked to the effect of laser amplification in excited dielectrics, and thus to the presence of conduction-band electrons, the latter can be directly related to the ultrafast formation of extremely long-lived self-trapped excitons. It is shown that, locally, the amplification can reach one order of magnitude. We discuss the temporal and spectral characteristics of the amplification as well as its dependencies on pump and probe fluences and form a complete picture within a tentative model.

We study general 2D fermionic topological orders enriched by the mirror symmetry with ${\mathcal{M}}^2=1$. It is known that certain mirror symmetry enriched fermionic topological orders (mirror SETs) are anomalous, in the sense that they cannot be realized in strict two dimensions but have to live on the surface of 3D topological crystalline superconductors. Mirror anomaly, or equivalently 3D topological crystalline superconductor, has a ${\mathbb{Z}}_{16}$ classification. In this work, we derive an explicit expression, namely, an anomaly indicator, for the ${\mathbb{Z}}_{16}$ mirror anomaly for general fermionic mirror SETs. This derivation is based on the recently developed folding approach, originally proposed for bosonic topological orders. We generalize it to fermion systems. Through this approach, we establish a direct bulk-boundary correspondence between surface fermionic topological orders and 3D bulk topological crystalline superconductors. In addition, during the derivation, we obtain some general properties of fermionic topological orders as well as a few constraints on the properties of fermionic mirror SETs.

Kitaev's sixteenfold way is a classification of exotic topological orders in which ${\mathbb{Z}}_2$ gauge theory is coupled to Majorana fermions of Chern number $C$. The 16 distinct topological orders within this class, depending on $C\mathrm{mod}16$, possess a rich variety of Abelian and non-Abelian anyons. We realize more than half of Kitaev's sixteenfold way, corresponding to Chern numbers 0, $\pm 1$, $\pm 2$, $\pm 3$, $\pm 4$, and $\pm 8$, in an exactly solvable generalization of the Kitaev honeycomb model. For each topological order, we explicitly identify the anyonic excitations and confirm their topological properties. In doing so, we observe that the interplay between lattice symmetry and anyon permutation symmetry may lead to a “weak supersymmetry” in the anyon spectrum. The topological orders in our honeycomb lattice model could be directly relevant for honeycomb Kitaev materials, such as $\alpha \text{−}{\mathrm{RuCl}}_3$, and would be distinguishable by their specific quantized values of the thermal Hall conductivity.

Strain engineering has been well developed and widely used to manipulate properties of materials. For two-dimensional materials, via nanoindentation technique or depositing the materials onto flexible substrates, one usually triggers tensile strains. It would be intriguing to develop strategies to generate strains via noncontacting schemes, such as an optical field, to eliminate lattice damage and additional interactions. Here we theoretically and computationally illustrate an optomechanical approach (referred to as optostriction), which could induce intrinsic strains in materials. Taking the well-studied transition metal dichalcogenide monolayers as examples, we predict a large in-plane optostriction with strong anisotropy, owing to their unique directional band transition strength. This optically driven strain method can avoid direct and invasive mechanical contacts with materials, which is easily accessible and guarantees the reversibility of materials. Rather than nanoindentation technique and other similar methods, this optomechanical strain can be either tensile or compressive. Owing to its intrinsicality, compressive strains are robust without suffering Euler's instability. In-plane inhomogeneous strains can be easily achieved via illuminating a Gaussian beam onto the material, adding an interesting approach to realize and measure in-plane optoflexoelectricity. Unlike conventional electric field inducing strains in piezoelectrics, no symmetry constraints are required.

The ($2+1$)-dimensional ($2+1\mathrm{D}$) topological order can be characterized by the mapping-class-group representations for Riemann surfaces of genus 1, genus 2, etc. In this paper, we use those representations to determine the possible gapped boundaries of a $2+1\mathrm{D}$ topological order, as well as the domain walls between two topological orders. We find that mapping-class-group representations for both genus-1 and genus-2 surfaces are needed to determine the gapped domain walls and boundaries. Our systematic theory is based on the fixed-point partition functions for the walls (or the boundaries), which completely characterize the gapped domain walls (or the boundaries). The mapping-class-group representations give rise to conditions that must be satisfied by the fixed-point partition functions, which leads to a systematic theory. Such conditions can be viewed as bulk topological order determining the (noninvertible) gravitational anomaly at the domain wall, and our theory can be viewed as finding all types of the gapped domain wall given a (noninvertible) gravitational anomaly. We also developed a systematic theory of gapped domain walls (boundaries) based on the structure coefficients of condensable algebras.

We develop a theory for a type of disorder in condensed matter systems arising from local twist-angle fluctuations in two strongly coupled van der Waals monolayers twisted with respect to each other to create a flat-band moiré superlattice. The paradigm of “twist-angle disorder” arises from the currently ongoing intense research activity in the physics of twisted bilayer graphene. In experimental samples of pristine twisted bilayer graphene, which are nominally free of impurities and defects, the main source of disorder is believed to arise from the unavoidable and uncontrollable nonuniformity of the twist angle across the sample. To address this physics of twist-angle disorder, we develop a real-space, microscopic model of twisted bilayer graphene where the angle enters as a free parameter. In particular, we focus on the size of single-particle energy gaps separating the miniband from the rest of the spectrum, the Van Hove peaks, the renormalized Dirac cone velocity near charge neutrality, and the minibandwidth. We find that the energy gaps and minibandwidth are strongly affected by disorder while the renormalized velocity remains virtually unchanged. We discuss the implications of our results for the ongoing experiments on twisted bilayer graphene. Our theory is readily generalized to future studies of twist-angle disorder effects on all electronic properties of moiré superlattices created by twisting two coupled van der Waals materials with respect to each other.

A spin current—a flow of spin angular momentum—can be carried either by spin-polarized free electrons or by magnons, the quanta of a moving collective oscillation of localized electron spins, i.e., a spin wave. Traditionally, it was assumed that a spin wave in a magnetic film with spin-sink-free surfaces can transfer energy and angular momentum only along its propagation direction. In this work, using Brillouin light-scattering spectroscopy in combination with a theory of dipole-exchange spin-wave spectra, we show that in obliquely magnetized free magnetic films, the in-plane propagation of spin waves is accompanied by a transverse spin current along the film normal without any corresponding transverse transport of energy.

Monolayers of transition metal dichalcogenides (TMDCs) are promising materials for valleytronic applications, since they possess two individually addressable excitonic transitions at the nonequivalent $K$ and $K^{\prime }$ points with different spins, selectively excitable with light of opposite circular polarization. Here, it is of crucial importance to understand the elementary processes determining the lifetime of optically injected valley excitons. In this study, we perform microscopic calculations based on a Heisenberg equation of motion formalism to investigate the efficiency of the intervalley coupling in the presence (W-based TMDCs) and absence (Mo-based TMDCs) of energetically low-lying momentum-dark exciton states after pulsed excitation. While we predict a spin polarization lifetime on the order of some hundreds of femtoseconds in the absence of low-lying momentum-dark states, we demonstrate a strong elongation of the spin-polarization lifetime in the presence of such states due to a suppression of the intervalley exchange coupling.

It is shown that a condensate of microcavity exciton-polaritons exhibits bistability between its two orthogonal linearly polarized components for varying nonresonant excitation power. A non-Hermitian splitting of these components results in two parity-symmetric fixed-point solutions of opposite polarization, making up the hysteresis branches. These solutions correspond to the lowest threshold linearly polarized mode, which dominates at low pump powers, and a cross-polarized mode, which appears due to nonlinear pinning at higher excitation powers. The spin symmetry of the solutions extends the nonresonant bistable operation of polariton condensates to the entire equatorial plane of the Poincaré sphere. The results pave the way towards development of tailored bistable, linearly polarized, coherent sources of light.

Bulk glasses exhibit extra vibrational modes at low energies, collectively known as the boson peak. The vibrational dynamics in nanoscale alumina glasses have an impact on the performance of qubits and other superconducting devices; however, the frequency of the boson peak has not been previously measured. Here we report neutron spectroscopy experiments on Al/${\mathrm{Al}}_2{\mathrm{O}}_3$ nanoparticles consisting of spherical metallic cores with a radii from 20 to 1000 nm surrounded by a 3.5-nm-thick alumina glass. A low-energy peak is observed at ${\omega }_{\text{BP}}$ = 2.8 $\pm$ 0.6 meV for highly oxidized particles, indicating an excess in the density of states. The intensity of the peak scales inversely with particle size and oxide fraction, indicating a surface origin, and is redshifted by 3 meV with respect to the van Hove singularity of $\gamma$-phase ${\mathrm{Al}}_2{\mathrm{O}}_3$ nanocrystals. Molecular-dynamics simulations of $\alpha -{\mathrm{Al}}_2{\mathrm{O}}_3, \gamma -{\mathrm{Al}}_2{\mathrm{O}}_3$ and $\alpha -{\mathrm{Al}}_2{\mathrm{O}}_3$ show that the observed boson peak is a signature of the ultrathin glass surface and the characteristic frequency is reduced compared to the peak in the bulk glass.

The spin-polarized even-denominator fractional quantum Hall (FQH) states in the second Landau level (LL), i.e., 5/2 and 7/2, may possess novel quasiparticle excitations obeying non-Abelian statistics. However, the spin polarization of the 7/2 FQH state has not been investigated experimentally and the spin polarization of the 5/2 FQH state from tilted-field experiments remains controversial. Using a piezodriven sample rotator with the lowest electron temperature down to 25 mK, we studied the energy gap of the even-denominator FQH states in the second LL by precise control of the tilted angles with a resolution less than 0.1°. We observed two different energy gap dependences on the in-plane magnetic field for 5/2, 7/2, other FQH states (7/3 and 8/3) in the second LL, and reentrant integer quantum Hall (RIQH) states in the third LL. Though the transition fields vary from states, their corresponding in-plane magnetic lengths are comparable to the quantum well thickness of the sample, which may result from the influence of the finite-thickness effect. At low in-plane magnetic fields, before the conjectured finite-thickness effect starts to dominate, the energy gaps of both 5/2 and 7/2 states show a nondecreasing behavior, supporting spin-polarized ground states. Our results also suggest that the 7/3, 8/3 FQH states, and the RIQH states in the third LL are spin polarized or partially spin polarized.