We propose a nonlocal manipulation method to build topological devices through emerging robust helical surface states in Z_2=0 topological systems. Specifically, in a ribbon of Z_2=0 Bernevig- Hughes-Zhang (BHZ) model with finite-size effect, if magnetic impurities are doped on the top (bottom) edge, the edge states on the bottom (top) edge can be altered according to the strengths and directions of these magnetic impurities. Consequently, the backscattering between the emerging robust helical edge states and gapped normal edge states due to finite-size confinement is also changed, which makes the system alternate between a perfect one-channel conductor and a perfect insulator. This effect allows us to fabricate topological devices with high on-off ratio. Moreover, it can also be generalized to 3D model and more realistic Cd3As2 type Dirac semimetals.
Topological electric quadrupole is a recently proposed concept that extends the theory of electric polarization of crystals to higher orders. Such a quadrupole phase supports topological states localized on both edges and corners. In this work, we show that in a quadrupole phase of honeycomb lattice, topological helical edge states and pseudo-spin-polarized corner states appear by making use of a pseudo-spin degree of freedom related to point group symmetry. Furthermore, we argue that a general condition for emergence of helical edge states in a (pseudo-)spinful quadrupole phase is mirror or t…
In this work, we study the disorder effect on topological metals that support a pair of helical edge modes deeply embedded inside the gapless bulk states. Strikingly, we predict that a quantum spin Hall (QSH) phase can be obtained from such topological metals without opening a global band gap. To be specific, disorder can lead to a pair of robust helical edge states which is protected by an emergent $Z_2$ topological invariant, giving rise to a quantized conductance plateau in transport measurements. These results are instructive for solving puzzles in {various transport experiments on QSH mat…
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.
The manipulation of the helical edge states of two-dimensional topological insulators is crucial for the development of technological applications. Recently, an important step forward, namely, the experimental realization of a quantum point contact between helical edges, has been accomplished. We theoretically predict that such a quantum point contact, in the presence of a time periodic applied electric field, is characterized by a topological quantum phase transition in the Floquet spectrum. Moreover, we show that it is possible to detect this dynamical topological quantum phase transition by…
We study the possibility of realizing robust helical surface states in $Z_2=0$ systems. We find that the combination of anisotropy and finite-size confinement leads to the emergence of robust helical edge states in both 2D and 3D $Z_2=0$ systems. By investigating an anisotropic Bernevig-Hughes-Zhang model in a finite sample, we demonstrate that the transport manifestation of the surface states is robust against non-magnetic disorder, resembling that of a $Z_2 = 1$ phase. Notably, the effective energy gap for the robust helical states can be efficiently engineered, allowing for potential applic…
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…
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.
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…
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 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 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.
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…
Recent research on disorder effects in topological phases in quasicrystalline systems has received much attention. In this work, by numerically computing the (spin) Bott index and the thermal conductance, we reveal the effects of disorder on a class D chiral topological superconductor and a class DIII time-reversal-invariant topological superconductor in a two-dimensional Ammann-Beenker tiling quasicrystalline lattice. We demonstrate that both the topologically protected chiral and helical Majorana edge modes are robust against weak disorder in the quasicrystalline lattice. More fascinating is…
This study investigates the topological behavior of a continuous elastic phononic structure characterized by a 3-term Kekulé distortion. The elastic waveguide consists of a hexagonal unit cell whose geometric dimensions are intentionally perturbed according to a generalized Kekulé scheme. The resulting structure exhibits an effective Hamiltonian that resembles a quantum spin Hall system, hence suggesting that the waveguide can support helical topological edge states. Using first-principles calculations, we show the existence of nondegenerate pseudospin states and a very peculiar 6-lobe pseudos…
Cascade of topological phase transitions and revival of topological zero modes in imperfect double helical liquids
Institute of Physics, Academia Sinica（中央研究院物理研究所）；Department of Electronics and Electrical Engineering, National Yang Ming Chiao Tung University（国立阳明交通大学电子工程学系）；Physics Division, National Center for Theoretical Sciences（国家理论科学中心物理组）
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 propose a framework to realize helical edge states in phononic systems using two identical lattices with interlayer couplings between them. A methodology is presented to systematically transform a quantum mechanical lattice which exhibits edge states to a phononic lattice, thereby developing a family of lattices with edge states. Parameter spaces with topological phase boundaries in the vicinity of the transformed system are illustrated to demonstrate the robustness to mechanical imperfections. A potential realization in terms of fundamental mechanical building blocks is presented for the h…
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…
The helical state is a fundamental prerequisite for many spintronics applications and Majorana zero mode engineering in nanoscopic semiconductors. Its existence in quasi-one-dimensional nanowires was predicted to be detectable as a characteristic reentrant behavior in the conductance, which in a typical two-terminal architecture may be difficult to distinguish from other possible phenomena such as Fabry-Perot oscillations. Here we present an alternative method of helical gap detection free of the mentioned ambiguity, and based on the nonlocal conductance measurements in a three-terminal juncti…
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…
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…
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…
Recent studies indicated that helical organic molecules, such as DNA and $α$-helical protein, can behave as Thouless quantum pumps when a rotating electric field is applied perpendicularly to their helical axes. Here we investigate the influence of long-range hoppings on this topological pumping of electrons in single-helical organic molecules. Under variation of the long-range hoppings governed by a decay exponent $μ$, we find an energy gap in the molecular band structure closes at a critical value $μ_c$ of the decay exponent and reopens for $μ$ deviating from $μ_c$. The relevant bulk bands i…
Nanowires with helical surface states represent key prerequisites for observing and exploiting phase-coherent topological conductance phenomena, such as spin-momentum locked quantum transport or topological superconductivity. We demonstrate in a joint experimental and theoretical study that gated nanowires fabricated from high-mobility strained HgTe, known as a bulk topological insulator, indeed preserve the topological nature of the surface states, that moreover extend phase-coherently across the entire wire geometry. The phase-coherence lengths are enhanced up to 5 $μ$m when tuning the wires…
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.
The physics of Majorana fermion occurs at the edge and interface of many one-dimensional quantum many body system with gapped excitation spectrum. We present the renormalization group equations for strongly interacting helical liquid. We present the results of both Majorana- Ising topological quantum phase transition and also Berezinskii-Kosterlitz-Thouless topological phase transition. We show that the Majorana-Ising topological quantum phase transition for non-interacting case is an exactly solvable line but in presence of interaction the system has no exactly solvable line. We study the eff…
One-dimensional helical liquids can appear at boundaries of certain condensed matter systems. Two prime examples are the edge of a quantum spin Hall insulator and the hinge of a three-dimensional second-order topological insulator. For these materials, the presence of a helical state at the boundary serves as a signature of their nontrivial electronic bulk topology. Additionally, these boundary states are of interest themselves, as a novel class of strongly correlated low-dimensional systems with interesting potential applications. Here, we review existing results on such helical liquids in se…
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…
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…
Mainstream among topological insulators, GaSb/InAs quantum wells present a broken gap alignment for the energy bands which supports the quantum spin Hall insulator phase and forms an important building block in the search of exotic states of matter. Such structures allow the band-gap inversion with electrons and holes confined in adjacent layers, providing a fertile ground to tune the corresponding topological properties. Using a full 3D 8-band ${\bf k}\cdot{\bf p}$ method we investigate the inverted band structure of GaSb/InAs/GaSb and InAs/GaSb/InAs multilayers and the behavior of the helica…
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 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 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…
The two-dimensional topological insulating phase has been experimentally discovered in HgTe quantum wells (QWs). The low-energy physics of two-dimensional topological insulators (TIs) is described by the Bernevig-Hughes-Zhang (BHZ) model, where the realization of a topological or a normal insulating phase depends on the Dirac mass being negative or positive, respectively. We solve the BHZ model for a mass domain configuration, analyzing the effects on the edge modes of a finite Dirac mass in the normal insulating region (soft-wall boundary condition). We show that at a boundary between a TI an…
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 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…
Weyl semimetals are gapless three-dimensional topological materials where two bands touch at even number of points in the Brillouin zone. In this work we study a zincblende lattice model realizing a time-reversal invariant Weyl semimetal. The bulk dynamics is decribed by twelve helical Weyl nodes. Surface states form a peculiar quasi two-dimensional helical metal fundamentally different from the Dirac form typical for topological insulators. Allowed direction of velocity and spin of low-energy surface excitations are locked to the cubic symmetry axes. The studied system illustrates general pro…
Chains of magnetic impurities placed on a superconducting substrate and forming helical spin order provide a promising venue for realizing a topological superconducting phase. An effective tight-binding description of such helical Shiba chains involves long-range (power-law) hopping and pairing amplitudes which induce an unconventional topological critical point. At the critical point, we find exponentially localized Majorana bound states with a short localization length unrelated to a topological gap. Away from the critical point, this exponential decay develops a power-law tail. Our analytic…
We propose a method that can consecutively modulate the topological orders or the number of helical edge states in ultrathin film semiconductors without a magnetic field. By applying a staggered periodic potential, the system undergoes a transition from a topological trivial insulating state into a non-trivial one with helical edge states emerging in the band gap. Further study demonstrates that the number of helical edge state can be modulated by the amplitude and the geometry of the electric potential in a step-wise fashion, which is analogous to tuning the integer quantum Hall conductance b…
Recent topological band theory distinguishes electronic band insulators with respect to various symmetries and topological invariants, most commonly, the time reversal symmetry and the $\rm Z_2$ invariant. The interface of two topologically distinct insulators hosts a unique class of electronic states -- the helical states, which shortcut the gapped bulk and exhibit spin-momentum locking. The magic and so far elusive property of the helical electrons, known as topological protection, prevents them from coherent backscattering as long as the underlying symmetry is preserved. Here we present an …
The ground state of charge neutral graphene under perpendicular magnetic field was predicted to be a quantum Hall topological insulator with a ferromagnetic order and spin-filtered, helical edge channels. In most experiments, however, an otherwise insulating state is observed and is accounted for by lattice-scale interactions that promote a broken-symmetry state with gapped bulk and edge excitations. We tuned the ground state of the graphene zeroth Landau level to the topological phase via a suitable screening of the Coulomb interaction with a SrTiO$_3$ high-$k$ dielectric substrate. We observ…
A topological insulator (TI) nanowire (NW), where the core is insulating and the 2D spin-helical Dirac fermion topological surface states (TSS) are circumferentially quantized into a series of 1D sub-bands, promises novel topological physics and applications. An axial magnetic flux (Φ) through the core drives periodic topological transitions in the surface sub-bands, changing from being all doubly-degenerate with a gapped Dirac point (DP) at integer (including zero) flux quanta (Φ$_0$ = h/e, with h being the Planck constant and e the electron charge), to contain a topologically-protected, non-…
Supermoiré domain-resolved effective Hamiltonians and valley topology in helical multilayer graphene
Seoul National University（首尔大学）；Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and BIST（加泰罗尼亚纳米科学和纳米技术研究所（ICN2，西班牙高等科学研究委员会和巴塞罗那独立系统大学））；University of Seoul（首尔大学）
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…
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.
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 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 $hc/2e$ …
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…
We report a theoretical study of electron transport along helical molecules under an external electric field, which is perpendicular to the helix axis of the molecule. Our results reveal that the topological states could appear in single-helical molecule and double-stranded DNA in the presence of the perpendicular electric field. And these topological states guarantee adiabatic charge pumping across the helical molecules by rotating the electric field in the transverse plane and the pumped current at zero bias voltage is quantized. In addition, the quantized current constitutes multiple platea…
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 …
