We consider a metasurface consisting of a square lattice of cylindrical antidots in a two-dimensional topological insulator (2DTI). Each antidot supports a degenerate Kramer's pair of eigenstates formed by the helical topological edge states. We show that the on-site Coulomb repulsion leads to the onset of the Mott insulator phase in the system in a certain range of experimentally relevant parameters. Intrinsic strong spin-orbit coupling characteristic for the 2DTI supports a rich class of the emerging low-energy spin Hamiltonians that can be emulated in the considered system, which makes it an appealing solid-state platform for quantum simulations of strongly correlated electron systems.

Time-periodic driving fields could endow a system with peculiar topological and transport features. In this work, we find dynamically controlled localization transitions and mobility edges in non-Hermitian quasicrystals via shaking the lattice periodically. The driving force dresses the hopping amplitudes between lattice sites, yielding alternate transitions between localized, mobility edge, and extended non-Hermitian quasicrystalline phases. We apply our Floquet engineering approach to five representative models of non-Hermitian quasicrystals, obtain the conditions of photon-assisted localization transitions and mobility edges, and find the expressions of Lyapunov exponents for some models. We further introduce topological winding numbers of Floquet quasienergies to distinguish non-Hermitian quasicrystalline phases with different localization nature. Our discovery thus extend the study of quasicrystals to non-Hermitian Floquet systems, and provide an efficient way of modulating the topological and transport properties of these unique phases.

The chiral hinge modes are the key feature of a second-order topological insulator in three dimensions. Here we propose a quadrupole index in combination of a slab Chern number in the bulk to characterize the flowing pattern of chiral hinge modes along the hinges at the intersection of the surfaces of a sample. We further utilize the topological field theory to present a picture of three-dimensional quantum anomalous Hall effect as a consequence of chiral hinge modes. The two bulk topological invariants can be measured in electric transport and magneto-optical experiments. In this way we establish the bulk-hinge correspondence in a three-dimensional second-order topological insulator.

The surfaces of intrinsic magnetic topological insulators (TIs) host magnetic moments exchange-coupled to Dirac electrons. We study the magnetic phases arising from tuning the electron density using variational and exact diagonalization approaches. In the dilute limit, we find that magnetic skyrmions are formed, which bind to electrons, leading to a skyrmion Wigner crystal phase while at higher densities spin spirals accompanied by chiral one-dimensional channels of electrons are formed. The binding of electrons to textures raises the possibility of manipulating textures with electrostatic gating. We determine the phase diagram capturing the competition of intrinsic spin-spin interactions and carrier density and comment on the possible application to experiments in magnetic TIs and spintronic devices such as skyrmion-based memory.

Within a Dirac model in $1+1$ dimensions, a prototypical model to describe low-energy physics for a wide class of lattice models, we propose a field-theoretical version for the representation of Wannier functions, the Zak-Berry connection, and the geometric tensor. In two natural Abelian gauges we present universal scaling of the Dirac Wannier functions in terms of four fundamental scaling functions that depend only on the phase $\gamma$ of the gap parameter and the charge correlation length $\xi$ in an insulator. The two gauges allow for a universal low-energy formulation of the surface charge and surface fluctuation theorem, relating the boundary charge and its fluctuations to bulk properties. Our analysis describes the universal aspects of Wannier functions for the wide class of one-dimensional generalized Aubry-André-Harper lattice models. In the low-energy regime of small gaps we demonstrate universal scaling of all lattice Wannier functions and their moments in the corresponding Abelian gauges. In particular, for the quadratic spread of the lattice Wannier function, we find the universal result $Za\xi /8$, where $Za$ is the length of the unit cell. This result solves a long-standing problem providing further evidence that an insulator is only characterized by the two fundamental length scales $Za$ and $\xi$. Finally, we discuss also non-Abelian lattice gauges and find that lattice Wannier functions of maximal localization show universal scaling and are uniquely related to the Dirac Wannier function of the lower band. In addition, via the winding number of the determinant of the non-Abelian transformation, we establish a bulk-boundary correspondence for the number of edge states up to the bottom of a certain band, which requires no symmetry constraints. Our results present evidence that universal aspects of Wannier functions and of the boundary charge are uniquely related and can be elegantly described within universal low-energy theories.

Motivated by the discovery of the quantum anomalous Hall effect in Cr-doped ${(\mathrm{Bi},\mathrm{Sb})}_2{\mathrm{Te}}_3$ thin films, we study the generic states for magnetic topological insulators and explore the physical properties for both magnetism and itinerant electrons. First-principles calculations are exploited to investigate the magnetic interactions between magnetic Co atoms adsorbed on the ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ (111) surface. Due to the absence of inversion symmetry on the surface, there are Dzyaloshinskii-Moriya-like twisted spin interactions between the local moments of Co ions. These nonferromagnetic interactions twist the collinear spin configuration of the ferromagnet and generate various magnetic orders beyond a simple ferromagnet. Among them, the spin spiral state generates alternating counterpropagating modes across each period of spin states, and the skyrmion lattice even supports a chiral mode around the core of each skyrmion. The skyrmion lattice opens a gap at the surface Dirac point, resulting in the anomalous Hall effect. These results may inspire further experimental investigation of magnetic topological insulators.

Electronic transport in Weyl semimetals is quite extraordinary due to the topological property of the chiral anomaly generating the charge pumping between two distant Weyl nodes with opposite chiralities under parallel electric and magnetic fields. Here, we develop a full nonequilibrium quantum transport theory of the chiral anomaly, based on the fact that the chiral charge pumping is essentially nothing but the Bloch oscillation. Specifically, by using the Keldysh nonequilibrium Green function method, it is shown that there is a rich structure in the chiral anomaly transport, including the negative magnetoresistance, the non-Ohmic behavior, the Esaki-Tsu peak, and finally the resonant oscillation of the dc electric current as a function of electric field, called the electric quantum oscillation. We argue that, going beyond the usual behavior of linear response, the non-Ohmic behavior observed in BiSb alloys can be regarded as a precursor to the occurrence of electric quantum oscillation, which is both topologically and energetically protected in Weyl semimetals.

We study the thermodynamic properties of topological Josephson junctions using a quantum spin Hall (QSH) insulator-based junction as an example. In particular, we propose that phase-dependent measurements of the heat capacity offer an alternative to Josephson-current measurements to demonstrate key topological features. Even in an equilibrium situation, where the fermion parity is not conserved, the heat capacity exhibits a pronounced double peak in its phase dependence as a signature of the protected zero-energy crossing in the Andreev spectrum. This double-peak feature is robust against changes of the tunneling barrier and thus allows one to distinguish between topological and trivial junctions. At short time scales, fermion parity is conserved and the heat capacity is $4\pi$ periodic in the superconducting phase difference. We propose a dispersive setup coupling the Josephson junction to a tank LC circuit to measure the heat capacity of the QSH-based Josephson junction sufficiently fast to detect the $4\pi$ periodicity. Although explicitly calculated for a short QSH-based Josephson junction, our results are also applicable to long as well as nanowire-based topological Josephson junctions.

We study the generalization of the three-dimensional two-band Hopf insulator to the case of many bands, where all the bands are separated from each other by band gaps. The obtained $\mathbb{Z}$ classification of such an $N$-band Hopf insulator is related to the quantized isotropic magnetoelectric coefficient of its bulk. The boundary of an $N$-band Hopf insulator can be fully gapped, and we find that there is no unique way of dividing a finite system into bulk and boundary. Despite this nonuniqueness, we find that the magnetoelectric coefficient of the bulk and the anomalous Hall conductivity of the boundary are quantized to the same integer value. We propose an experiment where the quantized boundary effect can be measured in a nonequilibrium state.

Topological edge modes, which are robust against disorders, have been used to enhance the spatial stability of lasers. Recently, it was revealed that topological lasers can be further stabilized using a topological phase in non-Hermitian photonic topological insulators. Here we propose a procedure to realize topologically protected modes extended over a $d$-dimensional bulk by introducing an imaginary gauge field. This generalizes the idea of zero-energy extended modes in the one-dimensional Su-Schrieffer-Heeger lattice into higher dimensional lattices, allowing a $d$-dimensional bulk mode that is topologically protected. Furthermore, we numerically demonstrate that the topological bulk lasing mode can facilitate high temporal stability superior to topological edge-mode lasers. Using an exemplified topological extended mode in the kagome lattice, we show that large regions of stability exist in its parameter space.

We propose an unconventional type of Hall effect in a topological Dirac semimetal with ferromagnetic electrodes. The topological Dirac semimetal itself has time-reversal symmetry, whereas attached ferromagnetic electrodes break it, causing the large Hall response. This induced Hall effect is a characteristic of the helical surface/edge states that arise in topological materials such as topological Dirac semimetals or quantum spin Hall insulators. We compute the Hall conductance/resistance and the Hall angle by using a lattice model with four-terminal geometry. For topological Dirac semimetals with four electrodes, the induced Hall effect occurs whether the current electrodes or the voltage electrodes are ferromagnetic. When the spins in electrodes are almost fully polarized, the Hall angle becomes as large as that of quantum Hall states or ideal magnetic Weyl semimetals. We show the robustness of the induced Hall effect against impurities and also discuss the spin injection and spin decay problems. This Hall response can be used to detect whether the magnetizations of the two ferromagnetic electrodes are parallel or antiparallel.

The interplay between nontrivial topological states of matter and strong electronic correlations is one of the most compelling open questions in condensed matter physics. Due to experimental challenges, there is an increasing desire to find more microscopic techniques to complement the results of more traditional experiments. In this work, we locally explore the Kondo insulator ${\mathrm{Sm}}_{1-x}{\mathrm{Gd}}_x{\mathrm{B}}_6$ by means of electron spin resonance (ESR) of ${\mathrm{Gd}}^{3+}$ ions at low temperatures. Our analysis reveals that the ${\mathrm{Gd}}^{3+}$ ESR line shape shows an anomalous evolution as a function of temperature, wherein for highly dilute samples $(x\approx 0.0002)$ the ${\mathrm{Gd}}^{3+}$ ESR line shape changes from a localized ESR local moment character to a diffusive-like character. Upon manipulating the sample surface with a focused ion beam we demonstrate, in combination with electrical resistivity measurements, that the localized character of the ${\mathrm{Gd}}^{3+}$ ESR line shape is recovered by increasing the penetration of the microwave in the sample. This provides compelling evidence for the contribution of surface or near-surface excitations to the relaxation mechanism in the ${\mathrm{Gd}}^{3+}$ spin dynamics. Our work brings new insights into the importance of nontrivial surface excitations in ESR, opening new routes to be explored both theoretically and experimentally.

We numerically investigate the topological phase transition induced purely by disorder in a spring-mass chain. We employ two types of disorders—chiral and random types—to explore the interplay between topology and disorder. By tracking the evolution of real-space topological invariants, we obtain the topological phase diagrams and demonstrate the bilateral capacity of disorder to drive topological transitions, from topologically nontrivial to trivial and vice versa. The corresponding transition is accompanied by the realization of a mechanical topological Anderson insulator. The findings from this study hint that the combination of disorder and topology can serve as an efficient control knob to manipulate the transfer of mechanical energy.