Lattice generalizations of fractional quantum Hall (FQH) systems, called fractional Chern insulators (FCIs), have been extensively investigated in strongly correlated systems. Despite many efforts, previous studies have not revealed all of the guiding principles for the FCI search. In this paper, we investigate a relationship between the topological band structure in the two-particle problem and the FCI ground states in the many-body problem. We first formulate the two-particle problem of a bosonic on-site interaction projected onto the lowest band of a given tight-binding Hamiltonian. We introduce a reduced Hamiltonian whose eigenvalues correspond to the two-particle bound-state energies. By using the reduced Hamiltonian, we define the two-particle Chern number and numerically check the bulk-boundary correspondence that is predicted by the two-particle Chern number. We then propose that a nontrivial two-particle Chern number of dominant bands roughly indicates the presence of bosonic FCI ground states at filling factor $\nu =1/2$. We numerically investigate this relationship in several tight-binding models with Chern bands and find that it holds well in most of the cases, albeit two-band models being exceptions. Although the two-particle topology is neither a necessary nor a sufficient condition for the FCI state as other indicators in previous studies, our numerical results indicate that the two-particle topology characterizes the degree of similarity to the FQH systems.

We theoretically study the electronic structure of interface states in twisted stacks of three-dimensional topological insulators. When the center of the surface Dirac cone is located at a midpoint of a side of the Brillouin zone boundary, we find that an array of nearly independent one-dimensional channels is formed by the interface hybridization of the surface states, even when the moiré pattern itself is isotropic. The two counterpropagating channels have opposite spin polarization, and they are robust against scattering by spin-independent impurities. The coupling between the parallel channels can be tuned by the twist angle. The unique one-dimensional states can be understood as effective Landau levels where the twist angle works as a fictitious magnetic field.

Entanglement is one of the most fundamental features of quantum systems. In this work, we obtain the entanglement spectrum and entropy of Floquet noninteracting fermionic lattice models and build their connections with Floquet topological phases. Topological winding and Chern numbers are introduced to characterize the entanglement spectrum and eigenmodes. Correspondences between the spectrum and topology of entanglement Hamiltonians under periodic boundary conditions and topological edge states under open boundary conditions are further established. The theory is applied to Floquet topological insulators in different symmetry classes and spatial dimensions. Our work thus provides a useful framework for the study of rich entanglement patterns in Floquet topological matter.

Skyrmion nucleation induced by spin-transfer torques at an interface of a topological insulator and a ferromagnetic insulator is investigated. Due to strong spin-orbit coupling on a surface of topological insulators, which enhances the effect of spin torques, efficient manipulation of skyrmions is expected, and therefore, topological insulators could provide the ideal platform to achieve high-performance skyrmionic devices. Using micromagnetic simulations and energetics, we evaluate properties of the skyrmion nucleation on a surface of topological insulators, such as nucleation time, critical electric field, and skyrmion numbers. We show that the nucleation time is inversely proportional to the applied electric field. We also identify the Gilbert damping and temperature dependencies of the critical field. Furthermore, we analytically evaluate the effect of the Dzyaloshinskii-Moriya interaction and demonstrate that the temperature dependence can be explained by the reduction of a magnon excitation gap due to the self-energy corrections.

Moiré materials have become one of the most active fields in material science in recent years due to their high tunability, and their unique properties emerge from the moiré-scale structure modulation. Here, we propose twisted bilayer ${\mathrm{Bi}}_2{\left({\mathrm{Te}}_{1-x}{\mathrm{Se}}_x\right)}_3$ as a moiré material where the moiré-scale modulation induces a topological phase transition. We show, in twisted bilayer ${\mathrm{Bi}}_2{\left({\mathrm{Te}}_{1-x}{\mathrm{Se}}_x\right)}_3$, a topological insulator domain and a normal insulator domain coexist in the moiré lattice structure, and edge states on the domain boundary make nearly flat bands that dominate the material properties. The edge states further contribute to a moiré-scale band inversion, resulting in moiré-scale topological states. There are corresponding moiré-scale edge states and they are so to speak “edge state from edge state,” which is a unique feature of twisted bilayer ${\mathrm{Bi}}_2{\left({\mathrm{Te}}_{1-x}{\mathrm{Se}}_x\right)}_3$. Our result not only proposes characteristic quantum phases in twisted bilayer ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ family, but also suggests the twisting of stacking-sensitive topological materials paves an avenue in the search for novel quantum materials and devices.

Twisted bilayer graphene (TBG) near “magic angles” has emerged as a rich platform for strongly correlated states of two-dimensional (2D) Dirac semimetals. Here we show that twisted bilayers of thin film magnetic topological insulators (MTIs) with large in-plane magnetization can realize flat bands near 2D Dirac nodes. Using a simple model for thin films of MTIs, we derive a continuum model for two such MTIs, twisted by a small angle with respect to each other. When the magnetization is in plane, we show that interlayer tunneling terms act as effective SU(2) vector potentials, which are known to lead to flat bands in TBG. We show that by changing the in-plane magnetization, it is possible to tune the twisted bilayer MTI band dispersion to quadratic band touching or to flat bands, similar to the TBG. If realized, this system can be a highly tunable platform for strongly correlated phases of two-dimensional Dirac semimetals.

We uncover a non-Hermitian skin mode in which the eigenmodes of a nonreciprocal topoelectrical (TE) heterojunction circuit array are localized at the heterojunction interface under both open boundary condition (OBC) and periodic boundary condition (PBC). This is in marked contrast to the conventional non-Hermitian skin effect (NHSE) in homogenous non-Hermitian systems that exists under OBC but vanishes in PBC. The interfacial non-Hermitian skin effect is induced when two non-Hermitian circuit chain segments with dissimilar NHSE decay lengths are cascaded together. It is shown analytically that the interfacial NHSE decay rates are directly associated with the asymmetric intracell couplings in the TE segments. Such nonreciprocal directional couplings can be realized in practical circuits by means of negative impedance converters with current inversion (INIC). In contrast to the conventional NHSE in homogeneous systems, the TE heterojunction circuit allows for a voltage profile localized at the interface, that is independent of the boundary conditions and whose decay length can be modulated by circuit parameters. Finally, the results presented are general and applicable to other analogous non-Hermitian platforms such as photonic and condensed matter nanoscale systems.

To simulate the dynamics of massless Dirac fermions in curved space-times with one, two, and three spatial dimensions, we construct tight-binding Hamiltonians with spatially varying hoppings. These models represent tilted Weyl semimetals where the tilting varies with position, in a manner similar to the light cones near the horizon of a black hole. We illustrate the gravitational analogies in these models by numerically evaluating the propagation of wave packets on the lattice and then comparing them to the geodesics of the corresponding curved space-time. We also show that the motion of electrons in these spatially varying systems can be understood through the conservation of energy and the quasiconservation of quasimomentum. This picture is confirmed by calculations of the scattering matrix, which indicate an exponential suppression of any noncontinuous change in the quasimomentum. Finally, we show that horizons in the lattice models can be constructed also at finite energies using specially designed tilting profiles.

We present a joint experimental and theoretical study of the driven Su-Schrieffer-Heeger model implemented by arrays of evanescently coupled plasmonic waveguides. Floquet theory predicts that this system hosts for suitable driving frequencies a topologically protected edge state that has no counterpart in static systems, the so-called anomalous Floquet topological $\pi$ mode. By using real- and Fourier-space leakage radiation microscopy in combination with edge and bulk excitation, we unequivocally identify the anomalous Floquet topological $\pi$ mode and study its frequency dependence.

Photonic higher-order topological insulators (HOTIs) based on kagome photonic crystals (PCs) possess rich physics of corner states for the unignorable long-range interactions. Theoretically, there should be multiple corner states, i.e., type I, antisymmetric type II, and symmetric type II corner states, in the kagome PCs. However, for the generation of some corner states, especially the symmetric type II corner states, it is necessary to obtain a large ratio of intercell coupling to intracell coupling, which makes the spacing between dielectric units very small and difficult to achieve experimentally. Here, we propose a scheme for the deterministic generation of multiple topological corner states based on an extremely expanded coupling condition. We construct an equilateral triangular cavity that consists of nontrivial unit cells in triangular PCs. All three topological corner states can exist robustly in the triangular cavity with large dielectric unit spacing. By establishing a tight-binding model for the nontrivial unit cell, we reveal that the extremely expanded coupling condition is the core physical mechanism for the deterministic generation of multiple corner states. The study provides a simple and deterministic method to generate multiple topological corner states, which has great potential in topological robust cavity, optical switches and lasers in integrated photonics on a silicon-on-insulator (SOI) or III-V active semiconductor platform.

The construction and classification of crystalline symmetry protected topological (SPT) phases in interacting bosonic and fermionic systems have been intensively studied in the past few years. Crystalline SPT phases are not only of conceptual importance, but also provide us great opportunities towards experimental realization since space group symmetries naturally exist for any realistic material. In this paper, we systematically classify the crystalline topological superconductors (TSC) and topological insulators (TI) in 2D interacting fermionic systems by using an explicit real-space construction. In particular, we discover an intriguing fermionic crystalline topological superconductor that can only be realized in interacting fermionic systems (i.e., not in free-fermion or interacting bosonic systems). Moreover, we also verify the recently conjectured crystalline equivalence principle for generic 2D interacting fermionic systems.

We investigate the impact on basic quantum transport properties of disorder-induced exceptional points (EPs) that emerge in a disorder-averaged Green's function description of two-dimensional Dirac semimetals with spin- or orbital-dependent potential scattering. Remarkably, we find that EPs may promote the nearly vanishing conductance of a finite sample at the Dirac point to a sizable value that increases with disorder strength. This striking behavior exhibits a strong directional anisotropy that is closely related to the Fermi arcs connecting the EPs. We corroborate our results by numerically exact simulations, thus revealing the fingerprints of characteristic non-Hermitian spectral features also on the localization properties of the considered systems. Finally, several candidates for the experimental verification of our theoretical analysis are discussed, including disordered electronic square-net materials and cold atoms in spin-dependent optical lattices.

We propose to use the Hall response of topological defects, such as merons and antimerons, to spin currents in two-dimensional magnetic insulator with in-plane anisotropy for identification of the Berezinskii-Kosterlitz-Thouless (BKT) transition in a transistorlike geometry. Our numerical results relying on a combination of Monte Carlo and spin dynamics simulations show transition from spin superfluidity to conventional spin transport, accompanied by the universal jump of the spin stiffness and exponential growth of the transverse vorticity current. We propose a superfluid spin transistor in which the spin and vorticity currents are modulated by changes in density of free topological defects, e.g., by injection of vorticity or by tuning the in-plane magnet across the BKT transition by changing the exchange interaction, magnetic anisotropy, or temperature.

We study the topological photonic states in one-dimensional lattices analog to the Su-Schrieffer-Heeger model beyond the dipole approximation. The electromagnetic resonances of the lattices supported by near-field interactions between the plasmonic nanoparticles are studied analytically with coupled dipole-quadrupole method. The topological phase transition in the bipartite lattices is determined by the change of Zak phase. Our results reveal the contribution of quadrupole moments to the near-field interactions and the band topology. It is found that the topological edge states in nontrivial lattices have both dipolar and quadrupolar nature. The quadrupolar edge states are not only orthogonal to the dipolar edge states, but also spatially localized at different sublattices. Furthermore, the quadrupolar topological edge states, which coexist at the same energy with the quadrupolar flat band have shorter localization length and hence smaller mode volume than the conventional dipolar edge states. The findings deepen our understanding in topological systems that involve higher-order multipoles, or in analogy to the wave functions in quantum systems with higher-orbital angular momentum, and may be useful in designing topological systems for confining light robustly and enhancing light-matter interactions.

Synchronization of coupled oscillators is a ubiquitous phenomenon found throughout nature. Its robust realization is crucial to our understanding of various nonlinear systems, ranging from biological functions to electrical engineering. On another front, in condensed matter physics, topology is utilized to realize robust properties like topological edge modes, as demonstrated by celebrated topological insulators. Here, we integrate these two research avenues and propose a nonlinear topological phenomenon, namely, topological synchronization, where only the edge oscillators synchronize while the bulk ones exhibit chaotic dynamics. We analyze concrete prototypical models to demonstrate the presence of positive Lyapunov exponents and Lyapunov vectors localized along the edge. As a unique characteristic of topology in nonlinear systems, we find that unconventional extra topological boundary modes appear at emerging effective boundaries. Furthermore, our proposal shows promise for spatially controlling synchronization, such as on-demand pattern designing and defect detection. The topological synchronization can ubiquitously appear in topological nonlinear oscillators and thus can provide a guiding principle to realize synchronization in a robust, geometrical, and flexible way.

This study demonstrates that the zeros of the diagonal components of Green functions are key quantities that can detect noninteracting topological insulators. We show that zeros of the Green functions traverse the band gap in the topological phases. The traverses induce the crosses of zeros, and the zeros' surface in the band gap, analogous to the Fermi surface of metals. By calculating the zeros of the microscopic models, we show the traverses of the zeros universally appear in all six classes of conventional noninteracting topological insulators. By utilizing the eigenvector-eigenvalue identity, which is a recently rediscovered relation in linear algebra, we prove that the traverses of the zeros in the bulk Green functions are guaranteed by the band inversions, which occur in the topological phases. The relevance of the zeros to detecting the exotic topological insulators such as the higher-order topological insulators is also discussed. For the Hamiltonians with the nearest-neighbor hoppings, we also show that the gapless edge state guarantees the zeros' surfaces in the band gap. The analysis demonstrates that the zeros can be used to detect a wide range of topological insulators and thus useful for searching new topological materials.

In search of materials with three-dimensional flat band dispersions, using ab initio computations we investigate how topological phases evolve as a function of hydrostatic pressure and uniaxial strain in two types of superlattices: HgTe/CdTe and HgTe/HgSe. In short-period HgTe/CdTe superlattices, our analysis unveils the presence of isoenergetic nodal lines, which could host strain-induced three-dimensional flat bands at the Fermi level without requiring doping, when fabricated, for instance, as core-shell nanowires. In contrast, HgTe/HgSe short-period superlattices are found to harbor a rich phase diagram with a plethora of topological phases. Notably, the unstrained superlattice realizes an ideal Weyl semimetal with Weyl points situated at the Fermi level. A small-gap topological insulator with multiple band inversions can be obtained by tuning the volume: under compressive uniaxial strain, the material transitions sequentially into a Dirac semimetal to a nodal-line semimetal, and finally into a topological insulator with a single band inversion.

We propose a correspondence between the description of emergent Lorentz symmetry in condensed-matter systems and the established general effective field theory for Lorentz violation in fundamental theories of spacetime and matter. This correspondence has potential implications in both directions. We illustrate the proposal by investigating its consequences for the spectral and transport properties of Dirac and Weyl semimetals. Particular realizations of this framework give rise to Dirac nodal spectra with nodal lines and rings. We demonstrate a bulk-boundary correspondence between bulk topological invariants and drumhead surface states of these Dirac nodal semimetals. We calculate their transport coefficients in leading-order perturbation theory, thereby characterizing the unconventional electromagnetic response due to small deviations from emergent Lorentz invariance. Some prospective future applications of the correspondence are outlined.