We show that two-terminal transport can measure the Luttinger liquid (LL) parameter $K$, in helical LLs at the edges of two dimensional topological insulators (TIs) with Rashba spin-orbit coupling. We consider a Coulomb drag geometry with two coplanar TIs and short-ranged spin-flip inter-edge scattering. Current injected into one edge loop induces circulation in the second, which floats without leads. In the low-temperature ($T \rightarrow 0$) perfect drag regime, the conductance is $(e^2/h)(2 K + 1)/(K + 1)$. At higher $T$ we predict a conductivity $\sim T^{-4K+3}$. The conductivity for a single edge is also computed.
Topological defects, such as domain walls and vortices, have long fascinated physicists. A novel twist is added in quantum systems like the B-phase of superfluid helium He$_3$, where vortices are associated with low energy excitations in the cores. Similarly, cosmic strings may be tied to propagating fermion modes. Can analogous phenomena occur in crystalline solids that host a plethora of topological defects? Here we show that indeed dislocation lines are associated with one dimensional fermionic excitations in a `topological insulator', a novel band insulator believed to be realized in the b…
We study Anderson localization in disordered helical conductors that are obtained from one-dimensional conductors with spin-orbit interaction and a magnetic field, or from equivalent systems. We call such conductors "quasi-helical" because the spins of the counterpropagating modes are not perfectly antiparallel and have a small spin-wavefunction overlap that is tunable by the magnetic field. Due to the overlap, disorder backscattering is possible and allows a localization transition. A conductor can pass through two localization transitions with increasing field, one from the conventionally lo…
We study the new phases of interacting Dirac matter that host novel Berry signatures. We predict a topological Lifshitz phase transition caused by the changes of a Dirac cone intersection from a semimetalic phase to helical insulating or metallic phases. These helical phases provide the examples of gapless topological phase where spectral gap is not required for a topological protection. To realize nodal helical phases one would need to consider isotropic infinite-range inter-particle interaction. This interaction could emerge because of a momentum conserving scattering of electron from a boso…
Two-dimensional superconductors with time-reversal symmetry have a Z_2 topological invariant, that distinguishes phases with and without helical Majorana edge states. We study the topological phase transition in a class-DIII network model, and show that it is associated with a metal-insulator transition for the thermal conductance of the helical superconductor. The localization length diverges at the transition with critical exponent nu approx 2.0, about twice the known value in a chiral superconductor.
Topological insulators (TI) are materials having an energy band gap in the bulk and conducting helical electronic states on the surface. The helical states are protected by time reversal symmetry thus are expected to be robust against static disorder scattering. In this work we report atomistic first principles analysis of disorder scattering in two-probe transport junctions made of three dimensional TI material Bi2Se3. The robustness of the device against disorder scattering is determined quantitatively. Examining many different scattering configurations, a general trend emerges on how strong…
Robustness of helical hinge states of three-dimensional weak second-order topological i sulators (WSOTIs) against disorders is studied. The pure WSOTI is obtained from a weak $\mathbb{Z}_2$ first-order topological insulator through a surface band inversion. Both bulk states and surface states in the WSOTI are gapped, and in-gap valley-momentum locked helical hinge states are topologically protected by the surface valley-Chern number. In the presence of weak disorders, helical hinge states are robust against disorders while the quantized conductance of the states is fragile due to the inter-val…
A workable model for describing dislocation lines introduced into a three-dimensional topological insulator is proposed. We show how fragile surface Dirac cones of a weak topological insulator evolve into protected gapless helical modes confined to the vicinity of dislocation line. It is demonstrated that surface Dirac cones of a topological insulator (either strong or weak) acquire a finite-size energy gap, when the surface is deformed into a cylinder penetrating the otherwise surface-less system. We show that when a dislocation with a non-trivial Burgers vector is introduced, the finite-size…
We derive and analyze the effective low-energy theory for interacting electrons in a cylindrical nanowire made of a strong topological insulator. Three different approaches provide a consistent picture for the band structure, where surface states forming inside the bulk gap correspond to one-dimensional bands indexed by total angular momentum. When a half-integer magnetic flux pierces the nanowire, we find a strongly correlated helical Luttinger liquid topologically protected against weak disorder. We describe how transport experiments can detect this state.
We consider the proximity effect between a singlet s-wave superconductor and the edge of a Quantum Spin Hall (QSH) topological insulator. We establish that Andreev reflection at a QSH edge state/superconductor interface is perfect while nonlocal Andreev processes through the superconductor are totally suppressed. We compute the corresponding conductance and noise.
Electrons on the surface of a strong topological insulator, such as Bi2Te3 or Bi1-xSnx, form a topologically protected helical liquid whose excitation spectrum contains an odd number of massless Dirac fermions. A theoretical survey and classification is given of the universal features, observable by the ordinary and spin-polarized scanning tunneling spectroscopy, in the interference patterns resulting from the quasiparticle scattering by magnetic and non-magnetic impurities in such a helical liquid. Our results confirm the absence of backscattering from non-magnetic impurities observed in rece…
Non-local pairing processes at the edge of a two-dimensional topological insulator in proximity to an $s$-wave superconductor are usually suppressed by helicity. However, additional proximity of a ferromagnetic insulator can substantially influence the helical constraint and therefore open a new conduction channel by allowing for crossed Andreev reflection (CAR) processes. We show a one-to-one correspondence between CAR and the emergence of odd-frequency triplet superconductivity. Hence, non-local transport experiments that identify CAR in helical liquids yield smoking-gun evidence for unconve…
The discovery of three-dimensional (3D) topological insulators opens a gateway to generate unusual phases and particles made of the helical surface electrons, proposing new applications using unusual spin nature. Demonstration of the helical electron transport is a crucial step to both physics and device applications of topological insulators. Topological insulator nanowires, of which spin-textured surface electrons form 1D band manipulated by enclosed magnetic flux, offer a unique nanoscale platform to realize quantum transport of spin-momentum locking nature. Here, we report an observation o…
We develop a theory of electron-photon interaction for helical edge channels in two-dimensional topological insulators based on zinc-blende-type quantum wells. It is shown that the lack of space inversion symmetry in such structures enables the electro-dipole optical transitions between the spin branches of the topological edge states. Further, we demonstrate the linear and circular dichroism associated with the edge states and the generation of edge photocurrents controlled by radiation polarization.
A non-Hermitian extension of a Chern insulator and its bulk-boundary correspondence are investigated. It is shown that in addition to the robust chiral edge states that reflect the nontrivial topology of the bulk (nonzero Chern number), anomalous helical edge states localized only at one edge can appear, which are unique to the non-Hermitian Chern insulator.
In the heterostructure composed of a topological insulator sandwiched by two s-wave superconductors, the time reversal invariant topological superconducting phase, possessing helical Majorana edge modes, is found to exist when the two s-wave superconductors form a Josephson junction with a pi phase shift. Based on such a heterostructure, a helical Dirac-Majorana interferometer is proposed to directly measure a unique transport signature of the helical Majorana modes. Furthermore, we envision how our proposal can be realized on the basis of existing materials such as Bi2Se3 or Bi2Te3 thin films…
We study spin susceptibility and magnetic order at the edges/surfaces of two-dimensional and three-dimensional topological insulators when the Fermi surface is nested. We find that due to spin-momentum locking as well as time-reversal symmetry, spin susceptibility at the nesting wavevector has a strong {\em helical} feature. It follows then, a {\em helical} spin density wave (SDW) state emerges at low temperature due to Fermi surface nesting. The helical feature of spin susceptibility also has profound impact on the magnetic order in magnetically doped surface of three dimensional topological …
We investigate theoretically the quantum phase transition (QPT) between the one-channel Kondo (1CK) and two-channel Kondo (2CK) fixed points in a quantum dot coupled to helical edge states of interacting 2D topological insulators (2DTI) with Luttinger parameter $0<K<1$. The model has been studied in Ref. 21, and was mapped onto an anisotropic two-channel Kondo model via bosonization. For K<1, the strong coupling 2CK fixed point was argued to be stable for infinitesimally weak tunnelings between dot and the 2DTI based on a simple scaling dimensional analysis[21]. We re-examine this model beyond…
Topological insulators are currently of considerable interest due to peculiar electronic properties originating from helical states on their surfaces. Here we demonstrate that the sound excited by helical particles on surfaces of topological insulators has several exotic properties fundamentally different from sound propagating in non-helical or even isotropic helical systems. Specifically, the sound may have strictly forward propagation absent for isotropic helical states. Its dependence on the anisotropy of the realistic surface-states is of distinguished behavior which may be used as an alt…
In an ideal topological insulator, the helical spin structure of surface electrons suppresses backscattering and thus can enhance surface conductivity. We investigate the effect of perpendicular magnetic field on the spin structure of electrons at the Fermi energy and calculate a magnetic-field dependent topological enhancement factor for different disorder potentials, ranging from short-range disorder to screened Coulomb potential. Within the Boltzmann approximation, the topological enhancement factor reaches its maximum value of 4 for a short-range disorder at zero magnetic field and approac…
Topological insulators are promising for spintronics and related technologies due to their spin-momentum-locked edge states, which are protected by time-reversal symmetry. In addition to the unique fundamental physics that arises in these systems, the potential technological applications of these protected states has also been driving TI research over the past decade. However, most known topological insulator materials naturally contain spinful nuclei, and their hyperfine coupling to helical edge states intrinsically breaks time-reversal symmetry, removing the topological protection and enabli…
We consider a four-terminal setup of a two-dimensional topological insulator (quantum spin Hall insulator) with local tunneling between the upper and lower edges. The edge modes are modeled as helical Luttinger liquids and the electron-electron interactions are taken into account exactly. Using perturbation theory in the tunneling, we derive the cumulant generating function for the inter-edge current. We show that different possible transport channels give rise to different signatures in the current noise and current cross-correlations, which could be exploited in experiments to elucidate the …
The quantum spin Hall (QSH) effect is the property of a new state of matter which preserves time-reversal, has an energy gap in the bulk, but has topologically robust gapless states at the edge. Recently, it has been shown that HgTe quantum wells realize this novel effect. In this work, we start from realistic tight-binding models and demonstrate the existence of the helical edge states in HgTe quantum wells and calculate their physical properties. We also show that 3d HgTe is a topological insulator under uniaxial strain, and show that the surface states are described by single-component mass…
We study dynamical mass generation and the resultant helical spin orders in topological Dirac and Weyl semimetals, including the edge states of quantum spin Hall insulators, the surface states of weak topological insulators, and the bulk materials of Weyl semimetals. In particular, the helical spin textures of Weyl semimetals manifest the spin-momentum locking of Weyl fermions in a visible manner. The spin-wave fluctuations of the helical order carry electric charge density; therefore, the spin textures can be electrically controlled in a simple and predictable manner.
We study bound states embedded into the continuum of edge states in two-dimensional topological insulators. These states emerge in the presence of a short-range potential of a structural defect coupled to the boundary. In this case the edge states flow around the defect and have two resonances in the local density of states. The bound state in continuum (BIC) arises due to an interference of the resonances when they are close to the degeneracy. We find the condition under which the BIC appears, study the spacial distribution of the electron density, and show that the BIC has a helical structur…
A two-dimensional time-reversal symmetric topological superconductor is a fully gapped system possessing a helical Majorana mode on the edges. This helical Majorana edge mode (HMEM), which is a Kramer's pair of two chiral Majorana edge modes in the opposite propagating directions, is robust under time-reversal symmetry protection. We propose a feasible setup and accessible measurement to provide the preliminary step of the HMEM realization by studying superconducting antiferromagnetic quantum spin Hall insulators. Since this antiferromagnetic topological insulator hosts a helical electron edge…
We theoretically study tunneling of Cooper pairs from a superconductor spanning a two-dimensional topological insulator strip into its helical edge states. The coherent low-energy electron-pair tunneling sets off positive current cross correlations along the edges, which reflect an interplay of two quantumentanglement processes. Most importantly, superconducting spin pairing dictates a Cooper pair partitioning into the helical edge liquids, which transport electrons in opposite directions for opposite spin orientations. At the same time, Luttinger-liquid correlations fractionalize electrons in…
We report a theoretical study of the quantized spin pump in a traditional two-parameter quantum pump device that is based on the helical edge states of a quantum spin Hall insulator. By introducing two time-dependent magnetizations out of phase as the pumping parameters, we found that when the Fermi energy resides in the energy gap opened by magnetization, an integer number of charges or spins can be pumped out in a pumping cycle and ascribed to the possible topological interface state born in between the two pumping potentials. The quantized pump current can be fully spin-polarized, spin-unpo…
We study supercurrent and proximity vortices in a Josephson junction made of disordered surface states of a three-dimensional topological insulator with a proximity induced in-plane helical magnetization. In a regime where the rotation period of helical magnetization is larger than the junction width, we find supercurrent 0-π crossovers as a function of junction thickness, magnetization strength, and parameters inherent to the helical modulation and surface states. The supercurrent reversals are associated with proximity induced vortices, nucleated along the junction width, where the number of…
A three-dimensional weak topological insulator (WTI) can be regarded as stacked layers of two-dimensional quantum spin-Hall insulators, each of which accommodates a one-dimensional helical edge mode. Massless Dirac electrons emerge on a side surface of WTIs as a consequence of the hybridization of such helical edge modes. We study the energy spectrum and transport of Dirac electrons on a side surface in the presence of step edges, which significantly modify the way of hybridization. It is shown that pseudo-helical modes with a nearly gapless linear dispersion can be created by manipulating ste…
Robustness of helical edge states in 2D topological insulators (TI) against strong interactions remains an intriguing issue. Here, by performing the first sign-free quantum Monte Carlo (QMC) simulation of the Kane-Mele-Hubbard-Rashba model which describes an interacting 2D TI with two-particle backscattering on edges, we verify that the gapless helical edge states are robust against a finite range of two-particle backscattering when the Coulomb repulsion is not strong. However, when the Coulomb repulsion is strong enough, the helical edge states can be gapped by infinitesimal two-particle back…
We study one-dimensional Kondo Lattices (KL) which consist of itinerant electrons interacting with Kondo impurities (KI) - localized quantum magnetic moments. We focus on KL with isotropic exchange interaction between electrons and KI and with a high KI density. The latter determines the principal róle of the indirect interaction between KI for the low energy physics. Namely, the Kondo physics becomes suppressed and all properties are governed by spin ordering. We present a first-ever comprehensive analytical theory of such KL at an arbitrary doping and predict a variety of regimes with differ…
Recent angle-resolved photoemission experiments have observed a proximity-induced superconducting gap in the helical surface states of a thin film of the 3D topological insulator Bi$_2$Se$_3$ grown on a superconducting NbSe$_2$ substrate. The superconducting coherence peaks in the electronic density of states are strongly suppressed when the topological insulator is doped with magnetic Mn impurities, which was interpreted as the complete destruction of helical superconductivity in the topological surface states. Motivated by these experiments, we explore a different possibility: gapless helica…
We report on the observation of a circular photogalvanic current excited by terahertz (THz) laser radiation in helical edge channels of HgTe-based 2D topological insulators (TIs). The direction of the photocurrent reverses by switching the radiation polarization from right-handed to left-handed one and, for fixed photon helicity, is opposite for the opposite edges. The photocurrent is detected in a wide range of gate voltages. With decreasing the Fermi level below the conduction band bottom, the current emerges, reaches a maximum, decreases, changes its sign close to the charge neutrality poin…
We study the effects of spatially localized breakdown of time reversal symmetry on the surface of a topological insulator (TI) due to proximity to a helical spin density wave (HSDW). The HSDW acts like an externally applied one-dimensional periodic(magnetic) potential for the spins on the surface of the TI, rendering the Dirac cone on the TI surface highly anisotropic. The decrease of group velocity along the direction $\hat{x}$ of the applied spin potential is twice as much as that perpendicular to $\hat{x}$. At the Brillouin zone boundaries (BZB) it also gives rise to new semi-Dirac points w…
Currently, much effort is being put into detecting unconventional p-wave superconductivity in Josephson junctions based on topological insulators (TIs). For that purpose we propose to use superconducting Klein tunneling, i.e. the reflectionless passage of Cooper pairs through a potential barrier in a gated ballistic junction. This phenomenon occurs due to the fact that the supercurrent is carried by helical Andreev bound states (ABSs) characterized by spin-momentum locking similar to the normal-state carriers. We derive the spectrum of the helical ABSs and the corresponding Josephson current f…
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…
Quantum spin Hall insulators are characterized by topologically protected counterpropagating edge states. Here we study the dynamical response of these helical edge states under a time-dependent flux biasing, in the presence of a heat bath. It is shown that the relaxation time of the edge carriers can be determined from a measurement of the dissipative response of topological insulator disks. The effects of various perturbations, including Zeeman coupling and disorder, are also discussed.
Collective plasmon excitations in a helical electron liquid on the surface of strong three-dimensional topological insulator are considered. The properties and internal structure of these excitations are studied. Due to spin-momentum locking in helical liquid on a surface of topological insulator, the collective excitations should manifest themselves as coupled charge- and spin-density waves.
Quantum spin Hall insulator is characterized by the helical edge states, with the spin polarization of electron being locked to its direction of motion. Although the edge-state conduction has been observed, unambiguous evidence of the helical spin texture is still lacking. Here, we investigate the coherent edge-state transport in an interference loop pinched by two point contacts. Due to the helical character, the forward inter-edge scattering enforces a $π$ spin rotation. Two successive processes can only produce a nontrivial $2π$ or trivial $0$ spin rotation, which can be controlled by the R…
Nonzero weak topological indices are thought to be a necessary condition to bind a single helical mode to lattice dislocations. In this work we show that higher-order topological insulators (HOTIs) can, in fact, host a single helical mode along screw or edge dislocations (including step edges) in the absence of weak topological indices. When this occurs, the helical mode is necessarily bound to a dislocation characterized by a fractional Burgers vector, macroscopically detected by the existence of a stacking fault. The robustness of a helical mode on a partial defect is demonstrated by an adia…
Topological insulators (TIs) are bulk insulators that possess robust helical conducting states along their interfaces with conventional insulators. A tremendous research effort has recently been devoted to TI-based heterostructures, in which conventional proximity effects give rise to a series of exotic physical phenomena. This paper reviews our recent works on the potential existence of topological proximity effects at the interface between a topological insulator and a normal insulator or other topologically trivial systems. Using first-principles approaches, we have established the tunabili…
A topological insulator is characterized by a dichotomy between the interior and the edge of a finite system: While the bulk has a non-zero energy gap, the edges are forced to sustain excitations traversing these gaps. Originally proposed for electrons governed by quantum mechanics, it has remained an important open question if the same physics can be observed for systems obeying Newton's equations of motion. Here, we report on measurements that characterize the collective behavior of mechanical oscillators exhibiting the phenomenology of the quantum spin hall effect. The phononic edge modes a…
We study backscattering of electrons and conductance suppression in a helical edge channel in two-dimensional topological insulators with broken axial spin symmetry in the presence of nonmagnetic point defects that create bound states. In this system the tunneling coupling of the edge and bound states results in the formation of composite helical edge states in which all four partners of both Kramers pairs of the conventional helical edge states and bound states are mixed. The backscattering is considered as a result of inelastic two-particle scattering of electrons, which are in these composi…
The edge states of a two-dimensional quantum spin Hall (QSH) insulator form a one-dimensional helical metal which is responsible for the transport property of the QSH insulator. Conceptually, such a one-dimensional helical metal can be attached to any scattering region as the usual metallic leads. We study the analytical property of the scattering matrix for such a conceptual multiterminal scattering problem in the presence of time reversal invariance. As a result, several theorems on the connectivity property of helical edge states in two-dimensional QSH systems as well as surface states of t…
We study the helical edge states of a two-dimensional topological insulator without axial spin symmetry due to the Rashba spin-orbit interaction. Lack of axial spin symmetry can lead to so-called generic helical edge states, which have energy-dependent spin orientation. This opens the possibility of inelastic backscattering and thereby nonquantized transport. Here we find analytically the new dispersion relations and the energy dependent spin orientation of the generic helical edge states in the presence of Rashba spin-orbit coupling within the Bernevig-Hughes-Zhang model, for both a single is…
Chiral edge state (CES) at zero magnetic field has already been realized in the magnetically doped topological insulator (TI). However, this scheme strongly relies on material breakthroughs, and in fact, most of the TIs cannot be driven into a Chern insulator in this way. Here, we propose to achieve the CESs in 2D TI/ferromagnetic insulator/TI sandwiched structures through spin-selective coupling between the helical edge states of the two TIs. Due to this coupling, the edge states of one spin channel are gapped and those of the other spin channel remain almost gapless, so that the helical edge…
We develop a theory of finite-temperature momentum-resolved tunneling spectroscopy (MRTS) for disordered, interacting two-dimensional topological-insulator edges. The MRTS complements conventional electrical transport measurement in characterizing the properties of the helical Luttinger liquid edges. Using standard bosonization technique, we study low-energy spectral function and the MRTS tunneling current, providing a detailed description controlled by disorder, interaction, and temperature, taking into account Rashba spin orbit coupling, interedge interaction and distinct edge velocities. Ou…
Silicene is a monolayer of silicon atoms forming a two-dimensional honeycomb lattice, which shares almost every remarkable property with graphene. The low energy structure of silicene is described by Dirac electrons with relatively large spin-orbit interactions due to its buckled structure. The key observation is that the band structure is controllable by applying the electric field to a silicene sheet. In particular, the gap closes at a certain critical electric field. Examining the band structure of a silicene nanoribbon, we demonstrate that a topological phase transition occurs from a topol…
The surface of a higher order topological insulator (HOTI) comprises a two-dimensional topological insulator (TI) with broken inversion symmetry, whose mass is determined by the microscopic details of the surface such as surface potentials and termination. It hosts a helical mode pinned to selected hinges where the surface gap changes its sign. We study the effect of perturbations that break time-reversal and particle-conservation on this helical mode, such as a Zeeman field and a proximate superconductor. We find that in contrast to the helical modes of inversion symmetric TIs, which are gapp…
We study coherent spin transport through helical edge states of topological insulator tunnel-coupled to metallic leads. We demonstrate that unpolarized incoming electron beam acquires finite polarization after transmission through such a setup provided that edges contain at least one magnetic impurity. The finite polarization appears even in the fully classical regime and is therefore robust to dephasing. There is also a quantum magnetic field-tunable contribution to the polarization, which shows sharp identical Aharonov-Bohm resonances as a function of magnetic flux - with the period $hc/2e$ …
We study the plasmon excitations and the electromagnetic response of the magnetically doped single layer and multilayer of ``helical metals'', which emerge at the surfaces of topological insulators. For the single layer case, we find a ``spin-plasmon'' mode with the rotating spin texture due to the combination of the spin-momentum locking of ``helical metals'' and the Hall response from magnetization. For the multilayers case, we investigate the electromagnetic response due to the plasmon excitations, including the Faraday rotation for the light propagating normal to the helical metal layers a…
We study the RKKY interaction mediated by the helical edge states of a quantum spin Hall insulator in the presence of the Rashba spin-orbital coupling induced by an external electric field and the electron-electron interaction. We show that in the presence of the Rashba coupling, the RKKY interaction induced by the helical edge states contains not only the Heisenberg-like and the Dzyaloshinskii-Moria terms but also the nematic-type term that is not present originally, with the range functions depending on the strength of the Rashba coupling. We also show that the electron-electron interaction …
