We study the electronic states that are formed due to the tunnel coupling between helical edge states (HESs) and bound states of nonmagnetic point defects in two-dimensional topological insulators in the general case of broken axial spin symmetry. It is found that the coupling of HESs and a single defect leads to the formation of composite HESs composed of the bound states and a set of the conventional HESs. Their spectral density near the defect has a resonance shifted relative to the energy level of the bound state. But of most importance is a long-range perturbation of the HESs around the defect, which is a cloud consisting of both Kramers partners of conventional edge states. Therefore each of the composite HESs contains both the right- and left-moving conventional HESs. The amplitude of this perturbation decreases inversely with the distance from the defect. In a system of many defects, this perturbation leads to a long-range coupling between bound states of different defects mediated by the HESs and causes amazing effects. We study these effects for a two-defect system where the proposed mechanism of indirect coupling leads to a splitting of the resonances of isolated defects even if the distance between them is very large. As a result an asymmetric structure of two-peak resonance arises that very unusually changes with the distance between the defects.
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…
Strong nonmagnetic impurities on the surface of three-dimensional topological insulators (TIs) generate localized resonance peaks close to the Dirac point. We show that this results in a strongly reduced critical Coulomb interaction strength to reach a magnetic surface state, following a Stoner-like criterion. Thus even weakly interacting TIs host a finite (local) magnetization around strong nonmagnetic impurities. The local magnetization gives rise to a global energy gap, linearly dependent on the maximum value of the magnetization but decreasing with reduced impurity concentration.
We propose theoretically a new effect, i.e. nonlinear planar Nernst effect (NPNE), in nonmagnetic topological insulator (TI) Bi2Te3 in the presence of an in-plane magnetic field. We find that the Nernst current scales quadratically with temperature gradient but linearly with magnetic field and exhibits a cosine dependence of the orientation of the magnetic field with respect to the direction of the temperature gradient. The NPNE has a quantum origin arising from the conversion of a nonlinear transverse spin current to a charge current due to a joint result of hexagonal warping effect, spin-mom…
We study the quasiparticle interference (QPI) patterns caused by scattering off nonmagnetic, magnetic point impurities, and edge impurities, separately, in a two dimensional helical liquid, which describes the surface states of a topological insulator. The unique features associated with hexagonal warping effects are identified in the QPI patterns of charge density with nonmagnetic impurities and spin density with magnetic impurities. The symmetry properties of the QPI patterns can be used to determine the symmetry of microscopic models. The Friedel oscillation is calculated for edge impuritie…
We investigate phonon spin transport in an insulating ferromagnet-nonmagnet-ferromagnet heterostructure. We show that the magnetoelastic interaction between the spins and the phonons leads to nonlocal spin transfer between the magnets. This transfer is mediated by a local phonon spin current and accompanied by a phonon spin accumulation. The spin conductance depends nontrivially on the system size, and decays over millimeter length scales for realistic material parameters, far exceeding the decay lengths of magnonic spin currents.
Spin current injection and spin accumulation near a ferromagnetic insulator (FI)/nonmagnetic metal (NM) bilayer film under a thermal gradient is investigated theoretically. Using the Fermi golden rule and the Boltzmann equations, we find that FI and NM can exchange spins via interfacial electron-magnon scattering because of the imbalance between magnon emission and absorption caused by either non-equilibrium distribution of magnons or non-equilibrium between magnons and electrons. A temperature gradient in FI and/or a temperature difference across the FI/NM interface generates a spin current w…
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.
At the interface between a nonmagnetic metal (NM) and a ferromagnetic insulator (FI) spin current can interact with the magnetization, leading to a modulation of the spin current. The interfacial exchange field at these FI-NM interfaces can be probed by placing the interface in contact with the spin transport channel of a lateral spin valve (LSV) device and observing additional spin relaxation processes. We study interfacial exchange field in lateral spin valve devices where Cu spin transport channel is in proximity with ferromagnetic insulator EuS (EuS-LSV) and yttrium iron garnet Y$_3$Fe$_5$…
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…
It is demonstrated that upon pulsed microwave excitation, the temporal behavior of a spin-wave induced inverse spin Hall voltage in a magnetic insulator-nonmagnetic metal structure is distinctly different from the temporal evolution of the directly excited spin-wave mode from which it originates. The difference in temporal behavior is attributed to the excitation of long-lived secondary spin-wave modes localized at the insulator-metal interface.
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 a kinetic equation for the electrons moving on the surface of a three-dimensional topological insulator. Due to the helical nature of the excitations backward scattering is suppressed in the collision integral, and the spin dynamics is entirely constrained by that of the charge. We further analyze the tunneling between the helical and a conventional metal or ferromagnet. We find that the tunnel resistance strongly depends on the angle between the magnetization in the ferromagnet and the current in the helical metal. A nonmagnetic layer on top of the helical metal amplifies the curren…
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.
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…
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.
Quantum anomalous Hall effect (QAHE) has been experimentally observed in magnetically doped topological insulators. However, ultra-low temperature (usually below 300 mK), which is mainly attributed to inhomogeneous magnetic doping, becomes a daunting challenge for potential applications. Here, a \textit{nonmagnetic}-doping strategy is proposed to produce ferromagnetism and realize QAHE in topological insulators. We numerically demonstrated that magnetic moments can be induced by nitrogen or carbon substitution in Bi$_2$Se$_3$, Bi$_2$Te$_3$, and Sb$_2$Te$_3$, but only nitrogen-doped Sb$_2$Te$_3…
A mechanism for phonon Hall effect (PHE) in non-magnetic insulators under an external magnetic field is theoretically studied. PHE is known in (para)magnetic compounds, where the magnetic moments and spin-orbit interaction play an essential role. In sharp contrast, we here show that a non-zero Berry curvature of acoustic phonons is induced by an external magnetic field due to the correction to the adiabatic Born-Oppenheimer approximation. This results in the finite thermal Hall conductivity $κ_H$ in nonmagnetic band insulators. Our estimate of $κ_H$ for a simple model gives $κ_H \sim 1.0\times…
We study in-gap electronic states induced by a nonmagnetic defect with short-range potential in two-dimensional topological insulators and trace their evolution as the distance between the defect and the boundary changes. The defect located far from the boundary is found to produce two bound states independently of the sign of its potential. The states are classified as electronlike and holelike. Each of these states can have two types of the spatial distribution of the electron density. The first-type states have a maximum of the density in the center and the second-type ones have a minimum. …
Magnetic doping is expected to open a band gap at the Dirac point of topological insulators by breaking time-reversal symmetry and to enable novel topological phases. Epitaxial (Bi$_{1-x}$Mn$_{x}$)$_{2}$Se$_{3}$ is a prototypical magnetic topological insulator with a pronounced surface band gap of $\sim100$ meV. We show that this gap is neither due to ferromagnetic order in the bulk or at the surface nor to the local magnetic moment of the Mn, making the system unsuitable for realizing the novel phases. We further show that Mn doping does not affect the inverted bulk band gap and the system re…
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…
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 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…
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…
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…
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.
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…
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…
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 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 $hc/2e$ …
The indirect exchange interaction between magnetic impurities located in the bulk of a two-dimensional topological insulator decays exponentially with the distance. The indirect exchange interaction for magnetic impurities mediated by the helical states at the edge of the topological insulator demonstrates behaviour which is typical for the Ruderman-Kittel-Kasuya-Yosida interaction in a one-dimensional metal. We have shown that interference between the bulk and edge states in the two-dimensional topological insulator results in existence of the unusual contribution to the indirect exchange int…
We show that with the help of spin-orbit coupling, nonlinear light-matter interactions can efficiently couple with spin and valley degrees of freedom. This revealed spin photogalvanic effect can generate the long-time pursued intrinsic pure spin current (PSC) in non-centrosymmetric nonmagnetic insulators. Different from the spin and valley Hall effect, such a photo-driven spin current is universal and can be generated without external bias field. Using first-principles simulation, we study monolayer transition metal dichalcogenides (TMDs) to demonstrate this effect and confirm an enhanced PSC …
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.
Two-dimensional topological insulators are characterized by gapped bulk states and gapless helical edge states, i.e. time-reversal symmetric edge states accommodating a pair of counter-propagating electrons. An external magnetic field breaks the time-reversal symmetry. What happens to the edge states in this case? In this paper we analyze the edge-state spectrum and longitudinal conductance in a two-dimensional topological insulator subject to a quantizing magnetic field. We show that the helical edge states exist also in this case. The strong magnetic field modifies the group velocities of th…
We compute the multifractal spectra associated to local density of states (LDOS) fluctuations due to weak quenched disorder, for a single Dirac fermion in two spatial dimensions. Our results are relevant to the surfaces of Z_2 topological insulators such as Bi_2Se_3 and Bi_2Te_3, where LDOS modulations can be directly probed via scanning tunneling microscopy. We find a qualitative difference in spectra obtained for magnetic versus non-magnetic disorder. Randomly polarized magnetic impurities induce quadratic multifractality at first order in the impurity density; by contrast, no operator exhib…
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 study collective excitations in a helical electron liquid on a surface of three-dimensional topological insulator. Electron in helical liquid obeys Dirac-like equation for massless particless and direction of its spin is strictly determined by its momentum. Due to this spin-momentum locking, collective excitations in the system manifest themselves as coupled charge- and spin-density waves. We develop quantum field-theoretical description of spin-plasmons in helical liquid and study their properties and internal structure. Value of spin polarization arising in the system with excited spin-pl…
Electrostatic Control Enables Robust Helical Edge Channel Transport in III-V Quantum Spin Hall Insulators
Julius-Maximilians-Universität Würzburg（维尔茨堡朱利叶斯-马克西米利安大学）；University of British Columbia（不列颠哥伦比亚大学）；Würzburg-Dresden Cluster of Excellence ctd.qmat（维尔茨堡-德累斯顿卓越集群 ctd.qmat）；Laboratoire Charles Coulomb (L2C)（夏尔·库仑实验室 (L2C)）；Université de Montpellier（蒙彼利埃大学）；CNRS（法国国家科学研究中心）；IES（电子与系统研究所）；Institut Universitaire de France（法兰西学院）；École Normale Supérieure, PSL（巴黎高等师范学院，PSL）
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…
It is predicted that electrons on the surface of a topological insulator can acquire a mass (massive Dirac fermion) by opening up a gap at the Dirac point when time-reversal symmetry is broken via the out-of-plane magnetization. We report photoemission studies on a series of topological insulator materials focusing on the spectral behavior in the vicinity of the Dirac node. Our results show that the spectral intensity is suppressed resulting in a "gap"-like feature in materials with or without any magnetic impurity or doping. The Zeeman gap in magnetically doped samples, expected to be rather …
Time reversal (T) invariant topological insulator is widely recognized as one of the fundamental discoveries in condensed matter physics, for which the most fascinating hallmark is perhaps a spin based topological protection, the total cancellation of scattering of conduction electrons with certain spins on matter surface. Recently, it has created a paradigm shift for topological insulators, from electronics to photonics, phononics as well as mechanics, bringing about not only involved new physics but also potential applications in robust wave transport. Despite the growing interests in realiz…
Based on a self-consistent $t$-matrix approximation, we explore the influence of magnetic and nonmagnetic doping on the surface electronic states and conductivity of topological insulators. We show that warping parameter has a crucial impact on the density of states and dc conductivity of the doped surfaces. As the warping strength is increased, the surface density of states at high energies is suppressed and the resonant states induced by impurities in the vicinity of the Dirac point gradually disappear. It is found that nonmagnetic impurities break electron-hole symmetry at low warping stren…
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 sin…
Localization of the helical edge states in quantum spin Hall insulators requires breaking time reversal invariance. In experiments this is naturally implemented by applying a weak magnetic field B. We propse a model based on scattering theory that describes the localization of helical edge states due to coupling to random magnetic fluxes. We find that the localization length is proportional to B^{2} when B is small, and saturates to a constant when B is sufficiently large. We estimate especially the localization length for the HgTe/CdTe quantum wells with known experimental parameters.
We study the spin texture of a generic helical liquid, the edge modes of a two-dimensional topological insulator with broken axial spin-symmetry. By considering honeycomb and square lattice realizations of topological insulators, we show that in all cases the generic behavior of a momentum-dependent rotation of the spin quantization axis is realized. Here we establish this mechanism also for disk geometries with continuous rotational symmetry. Finally, we demonstrate that the rotation of spin-quantization axis remains intact for arbitrary geometries, i.e. in the absence of any continuous symme…
We derived analytical results for the gapless edge states of two-dimensional topological insulators in the presence of electron-surface optical (SO) phonon interaction due to substrates. We followed an analytical algorithm, called Lee-Low-Pines variational approximation in the conventional polaron theory, to examine the substrate induced effects on both bulk and edge states of a two dimensional topological insulator within the frame work of Bernevig-Hughes-Zhang (BHZ) model. By implementing this algorithm, we propose a novel phonon-dressed BHZ Hamiltonian which allows one to investigate the ef…
In a topological insulator (TI) the character of electron transport varies from insulating in the interior of the material to metallic near its surface. Unlike, however, ordinary metals, conducting surface states in TIs are topologically protected and characterized by spin helicity whereby the direction of the electron spin is locked to the momentum direction. In this paper we review selected topics regarding recent theoretical and experimental work on electron transport and related phenomena in two-dimensional (2D) and three-dimensional (3D) TIs. The review provides a focused introductory dis…
