One of the hallmarks of bulk topology is the existence of robust boundary localized states. For instance, a conventional $d$ dimensional topological system hosts $d{-}1$ dimensional surface modes, which are protected by non-spatial symmetries. Recently, this idea has been extended to higher order topological phases with boundary modes that are localized in lower dimensions such as in the corners or in one dimensional hinges of the system. In this work, we demonstrate that a higher order topological phase can be engineered in a nonequilibrium state when the time-independent model does not possess any symmetry protected topological states. The higher order topology is protected by an emerging chiral symmetry, which is generated through the Floquet driving. Using both the exact numerical method and an effective high-frequency Hamiltonian obtained from the Brillouin-Wigner perturbation theory, we verify the emerging topological phase on a $π$-flux square lattice. We show that the localized corner modes in our model are robust against a chiral symmetry preserving perturbation and can be classified as `extrinsic' higher order topological phase. Finally, we identify a two dimensional topological invariant from the winding number of the corresponding sublattice symmetric one dimensional model. The latter model belongs to class AIII of ten-fold symmetry classification of topological matter.
Eigenenergies of a non-Hermitian system without parity-time symmetry are complex in general. Here, we show that the chiral boundary states of higher-dimensional (two-dimensional and three-dimensional) non-Hermitian topological insulators without parity-time symmetry can be Hermitian with real eigenenergies under certain conditions. Our approach allows one to construct Hermitian chiral edge and hinge states from non-Hermitian two-dimensional Chern insulators and three-dimensional second-order topological insulators, respectively. Such Hermitian chiral boundary channels have perfect transmission…
The generalized bulk-boundary correspondence predicts the existence of the chiral hinge states in three-dimensional second-order topological insulators (3DSOTIs), resulting in a quantized Hall effect in three dimensions. Chiral hinge states in Hermitian 3DSOTIs are characterized by the quantized transmission coefficients with zero fluctuations, even in the presence of disorders. Here, we show that chiral hinge transport in disordered non-Hermitian systems deviates from the paradigm of the Hermitian case. Our numerical calculations prove the robustness of hinge states of disordered non-Hermitia…
Where chiral modes should appear is an essential question for the quantum anomalous Hall (QAH) effect in three-dimensional topological insulators (3DTIs). In this Letter, we show that in a slab of ferromagnetic 3DTI subjected to a uniform exchange field normal to its top and bottom surfaces, the QAH effect creates a single chiral surface mode delocalized on the side faces. In a nonmagnetic 3DTI, analogously, delocalized helical modes consisting of a pair of oppositely propagating chiral surface modes are produced by the quantum spin Hall effect.
We propose a magnon realization of 3D topological insulator in the AIII (chiral symmetry) topological class. The topological magnon gap opens due to the presence of Dzyaloshinskii-Moriya interactions. The existence of the topological invariant is established by calculating the bulk winding number of the system. Within our model, the surface magnon Dirac cone is protected by the sublattice chiral symmetry. By analyzing the magnon surface modes, we confirm that the backscattering is prohibited. By weakly breaking the chiral symmetry, we observe the magnon Hall response on the surface due to open…
We study second-order topological insulators and semimetals characterized by chiral symmetry. We investigate topological phase transitions of a model for construction of the two-dimensional second-order topological insulators protected only by chiral symmetry. By the theory of the phase transitions, we propose a second-order topological semimetal and insulators with flat hinge bands in chiral-symmetric three-dimensional systems. The three-dimensional second-order topological phases can be obtained from the stacked two-dimensional second-order topological insulators with chiral symmetry. Moreov…
The robust quantization of observables in units of universal constants is a hallmark of topological phases. We show that chiral higher order topological insulators (HOTIs), bulk insulators with chiral hinge states, present two unusual features related to quantization. First, we show that circular dichroism is quantized to an integer or zero depending on the orientation of the sample. This probe locates the hinge states, and can be used to distinguish different types of chiral HOTIs. Second, we find that the average of the local Chern marker over a single surface, an observable related to the s…
The electronic transport properties in magnetically doped ultra-thin films of topological-insulators is investigated by using Landauer-buttiker formalism. The chiral selective tunneling is addressed in such systems which leads to transport gap and as a consequence current blocking. This quantum blocking of transport occurs when the magnetic states with opposite chirality are aligned energetically. This can be obsereved when an electron tunnels through a barrier or well of magnetic potential induced by the exchange field. It is proved and demonstrated that this chiral transition rule fails when…
We present a scheme to realize the chiral topological excitonic insulator in semiconductor heterostructures which can be experimentally fabricated with a coupled quantum well adjacent to twoferromagnetic insulating films. The different mean-field chiral topological orders, which are due to the change in the directions of the magnetization of the ferromagnetic films, can be characterized by the TKNN numbers in the bulk system as well as by the winding numbers of the gapless states in the edged system. Furthermore, we propose an experimental scheme to detect the emergence of the chiral gapless e…
In this article we consider the chiral Hall effect due to topologically protected kink states formed in topological insulators at boundaries between domains with differing topological invariants. Such systems include the surfaces of three dimensional topological insulators magnetically doped or in proximity with ferromagnets, as well as certain two dimensional topological insulators. We analyze the equilibrium charge current along the domain wall and show that it is equal to the sum of counter-propagating equilibrium currents flowing along external boundaries of the domains. In addition, we al…
Manifestation of chiral excitons on surfaces of topological insulator thin film with magnetically induced energy gap in the surface spectrum in magnetooptical Kerr and Faraday effects is analyzes. Excitonic contribution to a surface optical conductivity tensor is calculated. Chiral excitons contrary to conventional ones resonantly contribute to Hall conductivity due to lack of the symmetry between the states with opposite angular momentum. They can lead to considerable enhancement of Faraday angle and ellipticity of transmitted electromagnetic wave. Chiral excitons cause decrease of Kerr angle…
Recent magnetoconductance measurements performed on magnetic topological insulator candidates have revealed butterfly-shaped hysteresis. This hysteresis has been attributed to the formation of gapless chiral domain-wall bound states during a magnetic field sweep. We treat this phenomenon theoretically, providing a link between microscopic magnetization dynamics and butterfly hysteresis in magnetoconductance. Further, we illustrate how a spatially resolved conductance measurement can probe the most striking feature of the domain-wall bound states: their chirality. This work establishes a regime…
A non-Hermitian Chern insulator with gain/loss-type non-Hermiticity shows a peculiar gap closing; when a nontrivial Chern insulator phase changes to a gapless phase, conduction and valence bands are combined into one band owing to destabilization of chiral edge states. A previous recipe of non-Hermitian bulk-boundary correspondence is insufficient for this system since such a gap closing is beyond its scope. Here, we revise the recipe by taking the peculiar gap closing into account and apply it to the non-Hermitian Chern insulator. We demonstrate that the bulk-boundary correspondence holds in …
Three-dimensional higher-order topological insulators can have topologically protected chiral modes propagating on their hinges. Hinges with two co-propagating chiral modes can serve as a "beam splitter" between hinges with only a single chiral mode. Here we show how such a crystal, with Ohmic contacts attached to its hinges, can be used to realize a Mach-Zehnder interferometer. We present concrete calculations for a lattice model of a first-order topological insulator in a magnetic field, which, for a suitable choice of parameters, is an extrinsic second-order topological insulator with the r…
A family of semiconductors called as Chern band insulator are shown to host exciton bands with non-zero topological Chern integers and chiral exciton edge modes. Using a prototypical two-band Chern insulator model, we calculate a cross-correlation function to obtain the exciton bands and their Chern integers. The lowest exciton band acquires Chern integers such as $\pm 1$ and $\pm 2$ in electronic Chern insulator phase. The non-trivial topology can be experimentally observed both by non-local optoelectronic response of exciton edge modes and by a phase shift in the cross-correlation response d…
Selective bulk-boundary correspondence in higher-order topological insulators with anticommuting mirror and chiral symmetries
Indiana University（印第安纳大学）；Department of Physics, Indiana University（印第安纳大学物理系）；Quantum Science and Engineering Center, Indiana University（印第安纳大学量子科学与工程中心）
An intriguing phenomenon in topological semimetals and topological insulators is the negative magnetoresistance (MR) observed when a magnetic field is applied along the current direction. A prevailing understanding to the negative MR in topological semimetals is the chiral anomaly, which, however, is not well defined in topological insulators. We calculate the MR of a three-dimensional topological insulator, by using the semiclassical equations of motion, in which the Berry curvature explicitly induces an anomalous velocity and orbital moment. Our theoretical results are in quantitative agreem…
Topological insulators are insulators in the bulk but feature chiral energy propagation along the boundary. This property is topological in nature and therefore robust to disorder. Originally discovered in electronic materials, topologically protected boundary transport has since been observed in many other physical systems. Thus, it is natural to ask whether this phenomenon finds relevance in a broader context. We choreograph a dance in which a group of humans, arranged on a square grid, behave as a topological insulator. The dance features unidirectional flow of movement through dancers on t…
We study one-dimensional (1D) Floquet topological insulators with chiral symmetry going beyond the standard rotating wave approximation. The occurrence of many anticrossings between Floquet replicas leads to a dramatic extension of phase diagram regions with stable topological edge states (TESs). We present an explicit construction of all TESs in terms of a truncated Floquet Hamiltonian in frequency space, prove the bulk-boundary correspondence, and analyze the stability of the TESs in terms of their localization lengths. We propose experimental tests of our predictions in curved bilayer graph…
Chiral edge plasmons in quantum anomalous Hall insulators
Beijing Forestry University（北京林业大学）；Beijing Institute of Technology（北京理工大学）；Chinese Academy of Sciences（中国科学院）；University of Science and Technology of China（中国科学技术大学）
A magnetic domain boundary on the surface of a three-dimensional topological insulator is predicted to host a chiral edge state, but direct demonstration is challenging. Here, we used a scanning superconducting quantum interference device to show that current in a magnetized EuS/Bi2Se3 heterostructure flows at the edge when the Fermi level is gate-tuned to the surface band gap. We further induced micron-scale magnetic structures on the heterostructure, and detected a chiral edge current at the magnetic domain boundary. The chirality of the current was determined by magnetization of the surroun…
Starting with a description of the motivation underlying the analysis presented in this paper and a brief survey of the chiral anomaly, I proceed to review some basic elements of the theory of the quantum Hall effect in 2D incompressible electron gases in an external magnetic field, ("Hall insulators"). I discuss the origin and role of anomalous chiral edge currents and of anomaly inflow in 2D insulators with explicitly or spontaneously broken time reversal, i.e., in Hall insulators and "Chern insulators". The topological Chern-Simons action yielding the large-scale response equations for the …
We discuss several aspects of chiral optomagnonics in antiferromagnetic insulators by considering common symmetries between the electromagnetic field and spin excitations. This approach allows us to look at optical and magnetic materials from similar perspectives, and discuss useful analogies between them. We show that spin waves in collinear antiferromagnets and the electromagnetic field in vacuum are both invariant under the same eight-dimensional algebra of symmetry transformations. By such analogy, we can extend the concept of optical chirality to antiferromagnetic insulators, and demonstr…
A hybrid setup consisting of a superconductivity-proximitized quantum spin Hall (QSH) insulator and a quantum anomalous Hall (QAH) insulator is proposed for chiral injection of electrons into the Majorana bound state (MBS). An unexplored region of the phase space involving the exchange field induced boost of the helical edge state is then proposed for the detection of the MBS. 2-D transport simulations of our proposed setup is compared with the corresponding setup in the absence of the QAH region, when moderate disorder and a small but finite bulk out-of-plane magnetic field and a Rashba field…
Low energy excitation of surface states of a three-dimensional topological insulator (3DTI) can be described by Dirac fermions. By using a tight-binding model, the transport properties of the surface states in a uniform magnetic field is investigated. It is found that chiral surface states parallel to the magnetic field are responsible to the quantized Hall (QH) conductance $(2n+1)\frac{e^2}{h}$ multiplied by the number of Dirac cones. Due to the two-dimension (2D) nature of the surface states, the robustness of the QH conductance against impurity scattering is determined by the oddness and ev…
Chiral Majorana edge modes are theoretically proposed to perform braiding operations for the potential quantum computation. Here, we suggest a scheme to regulate trajectories of the chiral Majorana fermion based on a quantum anomalous Hall insulator (QAHI)-topological superconductor heterostructure. An applied external gate voltage to the QAHI region introduces a dynamical phase so that the outgoing Majorana fermions can be prominently tuned to different leads. The trajectory is mechanically analyzed and the electrical manipulation is represented by the oscillating transmission coefficients ve…
Notion of square-root topological insulators have been recently generalized to higher-order topological insulators. In two-dimensional square-root higher-order topological insulators, emergence of in-gap corner states are inherited from the squared Hamiltonian which hosts higher-order topology. In this paper, we propose that the martini lattice model serves as a concrete example of higher-order topological insulators. Furthermore, we also propose a suquare-root higher-order topological insulator based on the martini model. Specifically, we propose that the honeycomb lattice model with two-site…
Field-theoretical approach to Anderson localization in 2D disordered fermionic systems of chiral symmetry classes (BDI, AIII, CII) is developed. Important representatives of these symmetry classes are random hopping models on bipartite lattices at the band center. As was found by Gade and Wegner two decades ago within the sigma-model formalism, quantum interference effects in these classes are absent to all orders of perturbation theory. We demonstrate that the quantum localization effects emerge when the theory is treated non-perturbatively. Specifically, they are controlled by topological vo…
We extend the theory of dipole moments in crystalline insulators to higher multipole moments. In this paper, we expand in great detail the theory presented in Ref. 1, and extend it to cover associated topological pumping phenomena, and a novel class of 3D insulator with chiral hinge states. In quantum-mechanical crystalline insulators, higher multipole bulk moments manifest themselves by the presence of boundary-localized moments of lower dimension, in exact correspondence with the electromagnetic theory of classical continuous dielectrics. In the presence of certain symmetries, these moments …
Electrostatic gating and the interference of chiral Majoranas in thin slabs of magnetic topological insulators
Institute for Cross-Disciplinary Physics and Complex Systems IFISC (CSIC-UIB)（跨学科物理与复杂系统研究所）；Department of Physics, University of the Balearic Islands（巴利阿里大学物理系）
We demonstrate the dissipationless transport of the chiral edge state (CES) in the nanodevices of quantum anomalous Hall insulator candidate MnBi2Te4. The device presents a near-zero longitudinal resistance together with a quantized Hall plateau in excess of 0.97 h/e2 over a range of temperatures from very low up to the Neel temperature of 22 K. Each of four-probe nonlocal measurements gives near-zero resistance and two-probe measurements exhibit a plateau of +1 h/e2, while the results of three-probe nonlocal measurements depend on the magnetic field. This indicates non-dissipation as well as …
The quantized conductance plateaus and zero conductance fluctuation are the general consequence of electron transport in chiral edge states of Hermitian Chern insulators. Here we show that the physics of electron transport through chiral or helical edge channels becomes much richer when the non-Hermicity is allowed. In the presence of an unbalanced non-Hermicity where the chiral edge states have finite-lifetime, the conductance of the edge channels is not quantized, but its conductance fluctuation is zero. For the balanced non-Hermicity, however, the chiral edge states have infinite-lifetime, …
Square-root topological states are new topological phases, whose topological property is inherited from the square of the Hamiltonian. We realize the first-order and second-order square-root topological insulators in phononic crystals, by putting additional cavities on connecting tubes in the acoustic Su-Schrieffer-Heeger model and the honeycomb lattice, respectively. Because of the square-root procedure, the bulk gap of the squared Hamiltonian is doubled. In both two bulk gaps, the square-root topological insulators possess multiple localized modes, i.e., the end and corner states, which are …
The chirality associated with broken time reversal symmetry in magnetically doped topological insulators has important implications to the quantum transport phenomena. Here we report the anomalous Hall effect studies in Mn- and Cr-doped Bi$_2$Te$_3$ topological insulators with varied thickness and doping content. By tracing the chirality of the Hall loops, we find that the Mn-type anomalous Hall effect with clockwise chirality is strengthened by the reduction of film thickness, which is opposite to that of the Cr-type anomalous Hall effect with counterclockwise chirality. We provide a phenomen…
Polarization-sensitive devices rely on meta-materials to exhibit varying degrees of absorption of light of a given handedness. The chiral surface states of a topological insulator(TI) selectively absorb right and left circularly polarized light in the vicinity of the Dirac cone reaching its maximum of unity at the $ Γ$ point. In this letter, we demonstrate that a band gap open TI with C$_{2v}$ symmetry which is represented through a combination of Rashba and Dresselhaus Hamiltonians alters the preferential absorption of left and right circularly polarized light allowing a smooth variation of t…
We derive the equations of motion of a Domain Wall in a thin-film magnet coupled to the surface states of a Topological Insulator in the presence of of both an electric field along the Domain Wall and a magnetic field perpendicular to the junction. We show how the electric field acts as a chirality stabilizer holding off the appearance of Walker breakdown and enhancing the terminal velocity. We also propose a mechanism to reverse the Domain Wall chirality in a controllable manner by tuning the chiral current flowing through the Wall. An input from a weak perpendicular magnetic field is require…
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 demonstrate the correspondent connection of the chiral hinge modes to the quadrupole index and the slab Chern number, and present a picture of three-dimensional quantum anomalous Hall effect as a consequence of chiral hinge modes. The t…
The phenomenon of mesoscopic Spin-Hall effect reveals in a nonequilibrium spin accumulation (driven by electric current) at the edges of a ballistic conductor or, more generally, in the regions with varying electron density. In this paper we review our recent results on spin accumulation in ballistic two-dimensional semiconductor heterostructures with Rashba/Dresselhaus spin orbit interactions, and extend the method developed previously to predict the existince of spin-Hall effect on the surface of three-dimensional topological insulators. The major difference of the new Spin-Hall effect is it…
The electronic orders in magnetic and dielectric materials form the domains with different signs of order parameters. The control of configuration and motion of the domain walls (DWs) enables gigantic, nonvolatile responses against minute external fields, forming the bases of contemporary electronics. As an extension of the DW function concept, we realize the one-dimensional quantized conduction on the magnetic DWs of a topological insulator (TI). The DW of a magnetic TI is predicted to host the chiral edge state (CES) of dissipation-less nature when each magnetic domain is in the quantum anom…
We demonstrate that a sizable chiral charge pumping can be achieved at room temperature in graphene/Yttrium Iron Garnet (YIG) bilayer systems. The effect, which cannot be attributed to the ordinary spin pumping, reveals itself in the creation of a dc electric field/voltage in graphene as a response to the dynamic magnetic excitations (spin waves) in an adjacent out-of-plane magnetized YIG film. We show that the induced voltage changes its sign when the orientation of the static magnetization is reversed, clearly indicating the broken spatial inversion symmetry in the studied system. The streng…
We study the electronic transport across an electrostatically-gated lateral junction in a HgTe quantum well, a canonical 2D topological insulator, with and without applied magnetic field. We control carrier density inside and outside a junction region independently and hence tune the number and nature of 1D edge modes propagating in each of those regions. Outside the 2D gap, magnetic field drives the system to the quantum Hall regime, and chiral states propagate at the edge. In this regime, we observe fractional plateaus which reflect the equilibration between 1D chiral modes across the juncti…
Multiple chiral Majorana states in proximitized magnetic topological insulator heterostructures
Universidad Autónoma de Madrid（马德里自治大学）；Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid（马德里自治大学凝聚态物理中心（IFIMAC））；Instituto de Estructura de la Materia IEM-CSIC（CSIC物质结构研究所）；Instituto Nicolás Cabrera, Universidad Autónoma de Madrid（马德里自治大学尼古拉斯·卡布雷拉研究所）
Motivated by the recent experimental realizations of hyperbolic lattices in circuit quantum electrodynamics and the research interest in the non-Euclidean generalization of topological phenomena, we investigate the Chern insulator phases in a hyperbolic $\{8,3\}$ lattice, which is made from regular octagons ($8$-gons) such that the coordination number of each lattice site is $3$. Based on the conformal projection of the hyperbolic lattice into the Euclidean plane, i.e., the Poincaré disk model, by calculating the Bott index ($B$) and the two-terminal conductance, we reveal two Chern insulator …
Doping a topological insulator (TI) film with transition metal ions can break its time-reversal symmetry and lead to the realization of the quantum anomalous Hall (QAH) effect. Prior studies have shown that the longitudinal resistance of the QAH samples usually does not vanish when the Hall resistance shows a good quantization. This has been interpreted as a result of the presence of possible dissipative conducting channels in magnetic TI samples. By studying the temperature- and magnetic field-dependence of the magnetoresistance of a magnetic TI sandwich heterostructure device, we demonstrate…
We present a low-energy model describing the reconstruction of the electronic spectrum in twisted bilayers of honeycomb crystals with broken sublattice symmetry. The resulting moiré patterns are classified into two families with different symmetry. In both cases, flat bands appear at relatively large angles, without any magic angle condition. Transitions between them give rise to sharp resonances in the optical absorption spectrum at frequencies well below the gap of the monolayer. Owing to their chiral symmetry, twisted bilayers display circular dichroism, i.e., different absorption of left a…
