Quantum materials that host a flatband, such as pseudospin-1 lattices and magic-angle twisted bilayer graphene, can exhibit drastically new physical phenomena including unconventional superconductivity, orbital ferromagnetism, and Chern insulating behaviors. We report a surprising class of electronic in-gap edge states in pseudospin-1 materials without the conventional need of band-inversion topological phase transitions or introducing magnetism via an external magnetic type of interactions. In particular, we find that, in two-dimensional gapped (insulating) Dirac systems of massive spin-1 quasiparticles, in-gap edge modes can emerge through only an electrostatic potential applied to a finite domain. Associated with these unconventional edge modes are spontaneous formation of pronounced domain-wall spin textures, which exhibit the feature of out-of-plane spin-angular momentum locking on both sides of the domain boundary and are quite robust against boundary deformations and impurities despite a lack of an explicit topological origin. The in-gap modes are formally three-component evanescent wave solutions, akin to the Jackiw-Rebbi type of bound states. Such modes belong to a distinct class due to the following physical reasons: three-component spinor wave function, unusual boundary conditions, and a shifted flatband induced by the external scalar potential. Not only is the finding of fundamental importance, but it also paves the way for generating highly controllable in-gap edge states with emergent spin textures using the traditional semiconductor gate technology. Results are validated using analytic calculations of a continuum Dirac-Weyl model and tight-binding simulations of realistic materials through characterizations of local density of state spectra and resonant tunneling conductance.

Four-dimensional quantum Hall (QH) models usually rely on synthetic dimensions for their simulation in experiment. Here, we study a QH system which features a nontrivial configuration of three-dimensional Weyl cones on its boundaries. We propose a three-dimensional analog of this model in the form of a dissipative Weyl semimetal (WSM) described by a non-Hermitian (NH) Hamiltonian, which in the long-time limit manifests the anomalous boundary physics of the four-dimensional QH model in the bulk spectrum. The topology of the NH WSM is captured by a three-dimensional winding number whose value is directly related to the total chirality of the surviving Weyl nodes. Upon taking open boundary conditions, instead of Fermi arcs, we find exceptional points with an order that scales with system size.

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 predict the existence of non-Hermitian topologically protected end states in a one-dimensional exciton-polariton condensate lattice, where topological transitions are driven by the laser pump pattern. We show that the number of end states can be described by a Chern number and a topological invariant based on the Wilson loop. We find that such transitions arise due to enforced exceptional points which can be predicted directly from the bulk Bloch wave functions. This allows us to establish a new type of bulk-boundary correspondence for non-Hermitian systems and to compute the phase diagram of an open chain analytically. Finally, we demonstrate topological lasing of a single end mode in a realistic model of a microcavity lattice.

Topological insulators are materials with spectral bands associated with an integer-valued index, manifesting through quantized bulk phenomena and robust boundary effects. In this Rapid Communication, we demonstrate that higher-order topological insulators are descendants from a high-dimensional chiral semimetal. Specifically, we apply dimensional reduction to an ancestor four-dimensional Chern insulator, and obtain two-dimensional (2D) second-order topological insulators when the former becomes chiral. Correspondingly, we derive the quantized charge accumulation at the corners of the 2D descendants and relate it to the topological index—the second Chern number—of the ancestor model. Our results provide a clear connection between the boundary states of higher-order topological insulators and topological pumps—the latter being dynamical realizations of the quantum Hall effect in high dimensions.

Anderson localization in two-dimensional topological insulators takes place via the so-called levitation and pair annihilation process. As disorder is increased, extended bulk states carrying opposite topological invariants move towards each other in energy, reducing the size of the topological gap, eventually meeting and localizing. This results in a topologically trivial Anderson insulator. Here, we introduce the anomalous levitation and pair annihilation, a process unique to periodically driven, or Floquet, systems. Due to the periodicity of the quasienergy spectrum, we find it is possible for the topological gap to increase as a function of disorder strength. Thus, after all bulk states have localized, the system remains topologically nontrivial, forming an anomalous Floquet-Anderson insulator (AFAI) phase. We show a concrete example for this process, adding disorder via on-site potential “kicks” to a Chern insulator model. By changing the period between kicks, we can tune which type of (conventional or anomalous) levitation and annihilation occurs in the system. We expect our results to be applicable to generic Floquet topological systems and to provide an accessible way to realize AFAIs experimentally, without the need for multistep driving schemes.

We investigate theoretically the dynamics of two quasidegenerate mechanical modes coupled through an open quantum two-level system. A mean-field approach shows that by engineering the retarded response of the two-level system with a coherent drive, the non-Hermitian mechanical spectrum exhibits an exceptional degeneracy point where the two modes coalesce. We show that this degeneracy can be exploited to manipulate the vectorial polarization of the mechanical oscillations. We find that adiabatically varying the detuning and the intensity of the drive induces a rotation of the mechanical polarization, which enables the topological and chiral actuation of one mode from the other. This topological manifestation of the degeneracy is further supported by quantum-jump Monte Carlo simulations to account for the strong quantum fluctuations due to the spontaneous emission of the two-level system. Our presentation focuses on a promising realization based on flexural modes of a carbon-nanotube cantilever coupled to a single-molecule electric dipole irradiated by a laser.

We demonstrate the equivalence between two distinct Luttinger liquid impurity problems. The first concerns a one-dimensional topological superconductor coupled at one end to the ends of two single-channel Luttinger liquids. The second concerns a point contact in the quantum spin Hall effect, where four helical Luttinger liquids meet at a point. Both of these problems have been studied previously and exhibit several stable phases, depending on the Luttinger parameter $K$, that can be characterized in terms of simple conformally invariant boundary conditions describing perfect normal (or Andreev) transmission or reflection. In addition, both problems exhibit critical points that are described by “intermediate” fixed points similar to those found in earlier studies of an impurity in a Luttinger liquid with spin. Though these two models have different symmetries and numbers of modes, we show they are equivalent and are related by a duality transformation, and we show that the nontrivial intermediate critical points are the same. In the noninteracting limit, $K=1$, the duality involves two distinct free fermion representations that are related by a nonlocal transformation that derives from the triality of $\text{SO}\left(8\right)$. Using the explicit translation between the two theories, we translate results from one problem to the other and vice versa. This allows us to make predictions about the topological superconductor–Luttinger liquid junction, including predictions about the global behavior of the critical conductance $G^{*}\left(K\right)$, as well predictions for the critical exponents and universal crossover scaling functions. In this paper, we introduce both models from scratch, using a common notation that facilitates their comparison, and we discuss in detail the dualities that relate them, along with their free fermion limits. We close with a discussion of open problems and future directions.

We consider a junction between two semi-infinite narrow ribbons of a two-dimensional (2D) topological insulator (TI) and calculate the electron current through the interface carried by one-dimensional (1D) edge states formed in the bulk band gap. In addition to an abrupt interface between ribbons, we also consider a configuration where one or two rectangular islands of finite length are sandwiched between these ribbons. We demonstrate that it is feasible to create “current-on” and “current-off” states by modifying the energy dispersion of 1D interface edge states and the resonant levels localized at the boundary of the island regions.

Nonlocality is an interesting topic in quantum physics and is usually mediated by some unique quantum states. Here we investigate a Weyl semimetal slab and find an exotic nonlocal correlation effect when placing two potential wells merely on the top and bottom surfaces. This correlation arises from the peculiar Weyl orbit in Weyl semimetals and is a consequence of the bulk-boundary correspondence in topological band theory. A giant nonlocal transport signal and a body breakdown by Weyl fermions are further uncovered, which can serve as signatures for verifying this nonlocal correlation effect experimentally. Our results extend another member in the nonlocality family and have potential applications for designing unique electric devices with fancy functions.

The emergence of photoinduced topological phases and their phase transitions is theoretically predicted in organic salt $\alpha$-(BEDT-TTF)${}_2{\mathrm{I}}_3$, which possesses inclined Dirac cones in its band structure. By analyzing a photodriven tight-binding model describing conduction electrons in the BEDT-TTF layer using the Floquet theorem, we demonstrate that irradiation with circularly polarized light opens a gap at the Dirac points, and the system eventually becomes a Chern insulator characterized by a quantized topological invariant. A rich phase diagram is obtained in the plane of amplitude and frequency of light, which contains Chern insulator, semimetal, and normal insulator phases. We find that the photoinduced Hall conductivity provides a sensitive means to detect the predicted phase evolutions experimentally. This work contributes towards developing the optical manipulation of electronic states in matter through broadening the range of target materials that manifest photoinduced topological phase transitions.

We theoretically show that the edge of a quantum spin Hall insulator (QSHI), attached to an insulating ferromagnet (FM), can realize a highly efficient spin-to-charge conversion. Based on a one-dimensional QSHI-FM junction, the electron dynamics on the QSHI edge is analyzed, driven by a magnetization dynamics in the FM. Under a large gap opening on the edge from the magnetic exchange coupling, we find that the spin injection into the QSHI edge gets suppressed while the charge current driven on the edge gets maximized, demanded by the band topology of the one-dimensional helical edge states.

Motivated by the recent experimental observations of quantum oscillations in the Kondo insulators ${\mathrm{SmB}}_6$ and ${\mathrm{YbB}}_{12}$, we study magneto-optical conductivity of Kondo insulators. We show that there exist nontrivial cyclotron resonance peaks in a frequency domain below the hybridization gap as a result of the characteristic Landau level structure of the system. Furthermore, these low-energy peaks are enhanced near the insulator-metal phase transition driven by an applied magnetic field and stable even at low temperatures. They are smoothly connected via the Kondo effect to resonance peaks for unhybridized conduction and $f$ electrons at high temperature. The nontrivial cyclotron resonance is a dynamical counterpart of quantum oscillations in static quantities, and through this intimate connection it will provide a useful insight for the latter.

We present a combined experimental and theoretical study of the surface vibrational modes of the topological insulator ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ with particular emphasis on the low-energy region below 10 meV that has been difficult to resolve experimentally. By applying inelastic helium atom scattering (HAS), the entire phonon dispersion was determined and compared with density functional perturbation theory (DFPT) calculations. The intensity of the phonon modes is dominated by a strong Rayleigh mode, in contrast to previous experimental works. Moreover, also at variance with recent reports, no Kohn anomaly is observed. These observations are in excellent agreement with DFPT calculations. Besides these results, the experimental data reveal—via bound-state resonance enhancement—two additional dispersion curves in the gap below the Rayleigh mode. They are possibly associated with an excitation of a surface electron density superstructure that we observe in HAS diffraction patterns. The electron-phonon coupling parameter $\lambda =0.23$, derived from our temperature-dependent Debye-Waller measurements, compares well with values determined by angular resolved photoemission or Landau level spectroscopy. Our work opens up a new perspective for terahertz (THz) measurements on two-dimensional (2D) materials as well as the investigation of subtle details (band bending, the presence of a 2D electron gas) with respect to the electron-phonon coupling.

A topological phase transition from a trivial insulator to a ${\mathbb{Z}}_2$ topological insulator requires the bulk band gap to vanish. In the case of noncentrosymmetric materials, these phases are separated by a gapless Weyl semimetal phase. However, at finite temperature, the gap is affected by atomic motion, through electron-phonon interaction, and by thermal expansion of the lattice. As a consequence, the phase space of topologically nontrivial phases is affected by temperature. In this paper, the pressure and temperature dependence of the indirect band gap of BiTeI is investigated from first principles. We evaluate the contribution from both electron-phonon interaction and thermal expansion, and show that their combined effect drives the topological phase transition towards higher pressures with increasing temperature. Notably, we find that the sensitivity of both band extrema to pressure and topology for electron-phonon interaction differs significantly according to their leading orbital character. Our results indicate that the Weyl semimetal phase width is increased by temperature, having almost doubled by 100 K when compared to the static lattice results. Our findings thus provide a guideline for experimental detection of the nontrivial phases of BiTeI and illustrate how the phase space of the Weyl semimetal phase in noncentrosymmetric materials can be significantly affected by temperature.

Full-shell nanowires (semiconducting nanowires fully coated with a superconducting shell) have been recently presented as an alternative means to create Majorana zero modes. In contrast to partially coated nanowires, it has been argued that full-shell nanowires do not require high magnetic fields and low densities to reach a putative topological regime. Here we present a theoretical study of these devices taking into account all the basic ingredients, including a charge distribution spread across the section of the nanowire, required to qualitatively explain recent experimental results (Vaitiekėnas et al., arXiv:1809.05513). We derive a criterion, dependent on the even-odd occupation of the radial subbands with zero angular momentum, for the appearance of Majorana zero modes. In the absence of angular subband mixing, these give rise to strong zero-bias anomalies in tunneling transport in roughly half of the system's parameter space under an odd number of flux quanta. Due to their coexistence with gapless subbands, the zero modes do not enjoy generic topological protection. Depending on the details of subband mixing in realistic devices, they can develop a topological minigap, acquire a finite lifetime, or even be destroyed.

We propose an exotic scenario in which topological superconductivity can emerge by doping strongly interacting fermionic systems whose spin degrees of freedom form a bosonic symmetry protected topological (SPT) state. Specifically, we study a one-dimensional (1D) example where the spin degrees of freedom form a spin-1 Haldane phase. Before doping, the charge and spin degrees of freedom are both gapped. Upon doping, the charge channel becomes gapless and is described by a $c=1$ compactified bosonic conformal field theory (CFT), while the spin channel remains gapped and still form a bosonic SPT state. Interestingly, an instability toward $p$-wave topological superconductivity is induced, coexisting with the symmetry protected spin edge modes that are inherited from the Haldane phase. This scenario is confirmed by density-matrix renormalization group simulation of a concrete lattice model, where we find that topological superconductivity is robust against interactions. We further show that by stacking doped Haldane phases an exotic 2D anisotropic superconductor can be realized, where the boundaries transverse to the chain direction are either gapless or spontaneously symmetry broken due to the Lieb-Schultz-Mattis (LSM) anomaly.

The origin of the planar Hall effect (PHE) in various nonmagnetic semimetals has become a subject of considerable interest, especially in regard to the chiral anomaly that several of these semimetals exhibit. Here, we report a large PHE that exceeds several mΩ cm over a wide range of temperature $T$ and magnetic field $B$ in micron-thick single-crystalline bismuth thin films grown by molecular beam epitaxy techniques. The angular dependence of the PHE and the related anisotropic magnetoresistance (AMR) show complex behaviors as a function of $B$ and $T$. At high temperatures and in modest magnetic fields, the PHE and AMR can be quantitatively explained by a semiclassical transport model based on the well-established elongated electron and hole pockets of the Fermi surface in bismuth. Although these results establish an anisotropic electronic orbital origin of the PHE, we find that when the electric current is oriented along the binary axis of bismuth, the PHE and AMR behaviors can be well described by a model based on the chiral anomaly in Weyl or Dirac semimetals. However, this model cannot account for these behaviors when the current is rather oriented along the bisectrix axis. Thus, the anisotropy of the PHE is a useful test to check on the validity of the chiral anomaly in semimetals.

Higher-order topological insulators are a new class of topological phases of matter, originally conceived for electrons in solids. It has been suggested that the ${\mathbb{Z}}_N$ Berry phase (Berry phase quantized into $2\pi /N$) is a useful tool to characterize the symmetry-protected topological states, whereas the experimental evidence is still elusive. Recently, topolectrical circuits have emerged as a simple yet very powerful platform for studying topological physics that are challenging to realize in condensed-matter systems. Here, we present an experimental observation of second-order corner states characterized by the ${\mathbb{Z}}_3$ Berry phase in topolectrical circuits. We demonstrate theoretically and experimentally that the localized second-order topological states are protected by a generalized chiral symmetry of tripartite lattices, and they are pinned to “zero energy.” By introducing extra capacitors within sublattices in the circuit, we are able to examine the robustness of the zero modes against both chiral-symmetry-conserving and breaking disturbances. Our Rapid Communication paves the way for testing exotic topological band theory by electrical-circuit experiments.

Recent advances in tuning electronic, magnetic, and topological properties of two-dimensional (2D) magnets have opened a new frontier in the study of quantum physics and promised exciting possibilities for future quantum technologies. In this study, we find that the dual-gate technology can well tune the electronic and topological properties of antiferromagnetic (AFM) even septuple-layer (SL) ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ thin films. Under an out-of-plane electric field that breaks $\mathcal{PT}$ symmetry, the Berry curvature of the thin film could be engineered efficiently, resulting in a huge change of anomalous Hall (AH) signal. Beyond the critical electric field, the double-SL ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ thin film becomes a Chern insulator with a high Chern number of 3. We further demonstrate that such 2D material can be used as an AFM switch via electric-field control of the AH signal. These discoveries inspire the design of low-power memory prototypes for future AFM spintronic applications.