Edge Of Topological Insulator Research Articles

Superconducting diode effect in two-dimensional topological insulator edges and Josephson junctions

The superconducting diode effect—the dependence of critical current on its direction—can arise from the simultaneous breaking of inversion and time-reversal symmetry in a superconductor and has gained interest for its potential applications in superconducting electronics. In this Letter, we study the effect in a two-dimensional topological insulator (2D TI) in both a uniform geometry as well as in a long Josephson junction. We show that in the presence of Zeeman fields, a circulating edge current enables a large non-reciprocity of the critical current. We find a maximum diode efficiency of 1 for the uniform 2D TI and (2−1)2≈0.17 for the long Josephson junction.

Impact of passivation on the Dirac cones of 2D topological insulators

Topological insulators have unique properties that make them promising materials for future implementation in next-generation electronic devices. However, topological insulators like stanene nanoribbons need to be passivated before they can be used in devices. We calculate the electronic band structure of stanene nanoribbons (SNRs) that are passivated by hydrogen (H), fluorine (F), chlorine (Cl), bromine (Br), iodine (I), or sodium (Na). We show that the difference between the electronegativity of the passivation material and the tin atoms defines the position of the Dirac cone of the topological insulator edge states. We develop a four-parameter tight-binding model based on the Kane–Mele model [Kane and Mele, Phys. Rev. Lett. 95, 226801 (2005); Kane and Mele, Phys. Rev. Lett. 95, 146802 (2005)]. The hopping parameters of the TB model are obtained by fitting the tight-binding model to the density functional theory (DFT) calculations. Finally, we demonstrate that the DFT band structures and the tight-binding model band structures are in good agreement with each other at low energies around the Dirac point, thereby capturing the complete physics of the passivated edge bands.

Quasistationary states in a quantum dot formed at the edge of a topological insulator by magnetic barriers with finite transparency

A model of quasistationary states is constructed for the one-dimensional edge states propagating along the edge of a two-dimensional topological insulator based on HgTe/CdTe quantum well in the presence of magnetic barriers with finite transparency. The lifetimes of these quasistationary states are found analytically and numerically via different approaches including the solution of the stationary Schrödinger equation with complex energy and the solution of the transmission problem for a double barrier structure. The results can serve as a guide for determining the parameters of magnetic barriers creating the quantum dots where the lifetimes for the broadened discrete levels are long enough for manipulation with their occupation numbers by external fields.

Elastic backscattering of edge electrons and light absorption on a smooth edge of a 2D topological insulator

2D topological insulator edge states are considered within the Volkov–Pankratov Hamiltonian. A smooth transition between a topological and ordinary insulator is assumed. The edge states are formed in the total gap of homogeneous 2D material. We found the energy spectrum, wave functions, together with the matrix elements of the impurity potential, and the velocity operator between these states. A pair of states have linear dispersion (the Weyl states), others have gapped Dirac spectra. Optical selection rules are found. It is stated that the Weyl states do not experience the backscattering, while the elastic scattering is permitted between the Dirac states or between the Weyl and Dirac states.

Spin Resonance in a Quantum Dot at the Edge of a Topological Insulator with the Inclusion of Continuum States

The dynamics of electronic states under the action of a periodic electric field applied to a quantum dot created by magnetic barriers at the one-dimensional edge of a two-dimensional topological insulator based on a HgTe/CdTe quantum well has been studied. A configuration with two discrete levels is considered and transitions to continuum states above barriers are taken into account. The frequency of oscillations of the discrete level populations has been calculated for various field amplitudes. It has been shown numerically and analytically that the inclusion of the continuous spectrum leads to a decrease in the total population of discrete levels in time. The characteristic times of this decrease corresponding to transitions to continuum have been determined. The dynamics of average values of the energy, spin projections, coordinates, local probability density, and local spin density has been calculated. Time-averaged local probability density current that describes the quantum dot escape at transitions to the continuous spectrum has been calculated. The results of this work can be useful for the design of new generations of nanoelectronics and spintronics devices based on topological insulators.

Enhanced Majorana bound states in magnetic chains on superconducting topological insulator edges

The most promising mechanisms for the formation of Majorana bound states (MBSs) in condensed matter systems involve one-dimensional systems (such as semiconductor nanowires, magnetic chains, and quantum spin Hall insulator (QSHI) edges) proximitized to superconducting materials. The choice between each of these options involves trade-offs between several factors such as reproducibility of results, system tunability, and robustness of the resulting MBS. In this article, we propose that a combination of two of these systems, namely a magnetic chain deposited on a QSHI edge in contact with a superconducting surface, offers a better choice of tunability and MBS robustness compared to magnetic chain deposited on bulk. We study how the QSHI edge interacts with the magnetic chain, and see how the topological phase is affected by edge proximity. We show that MBSs near the edge can be realized with lower chemical potential and Zeeman field than the ones inside the bulk, independently of the chain's magnetic order (ferromagnetic or spiral order). Different magnetic orderings in the chain modify the overall phase diagram, even suppressing the boundless topological phase found in the bulk for chains located at the QSHI edge. Moreover, we quantify the "quality" of MBSs by calculating the Majorana Polarization (MP) for different configurations. For chains located at the edge, the MP is close to its maximum value already for short chains. For chains located away from the edge, longer chains are needed to attain the same quality as chains located at the edge. The MP also oscillates in phase with the in-gap states, which is relatively unexpected as peaks in the energy spectrum corresponds to stronger overlap of MBSs.

The emergence of bound states in a superconducting gap at the topological insulator edge

We consider the edge of a superconducting topological insulator with the impurity in the presence of the Zeeman field. We analytically prove that in the trivial phase two Andreev bound states (ABSs) arise with energies moving from the superconducting gap edges to zero forming two Majorana-like bound states, as the impurity strength varies from 0 to ±2. When the Zeeman field is locally perturbed, ABSs arise both in the trivial and topological phases, but in the topological phase ABSs with energy near the gap edges cannot transform into Majorana bound states and vice versa.

The edge states properties of the topological insulator with fermion path nonanalyticity points located at the edge

The edge states properties of a finite-size 2D topological insulator (TI) with the open boundary conditions in both directions are studied. It is shown that fermion path nonanalyticity points appearing on the edge of finite-size TI cause a nonuniform edge state distribution along the TI edge. The character of this distribution depends substantially on the edge state’s energy position in the bulk band gap. The edge state with the energy in the middle of the gap tends to be located in the corners between two nonparallel edges of the system, while the edge states with the energy close to the bulk band edge avoid the corners. The monotonic transition from one space distribution of the edge state wave function to another along the edge state’s band is observed. The mentioned edge state’s structure leads to the nonlinear current-voltage characteristic of the square-shaped TI with contacts connected with the corners of the device. It opens the possibility to control the current with the gate voltage and is useful for construction the nano-size devices. For the edge states with energy in the middle of a bulk gap, the vortex structure of the probability flux located near corners is found.

(Invited) 2D-Metals: From Synthesis to Quantum Phenomena

Quantum materials (QMats) are prime candidates for next-generation energy-efficient technologies, such as topological quantum computing, quantum sensing, and neuromorphic computing. While van der Waals 2D materials exhibit a compellingly wide range of exotic and potentially useful properties such as charge density waves, topological insulator edges, and superconductivity, one can also realize these properties by stabilizing new 2D allotropes of traditionally 3D superconductors and magnets. In this talk I will discuss our pioneering work in confinement heteroepitaxy (CHet) that enables the creation of 2D forms of 3D materials (e.g. 2D-Ga, In, Sn) and decouples the growth of the metals from other 2D layers, thereby enabling a new platform for creating artificial quantum lattices (AQLs) with atomically sharp interfaces and designed properties. As a specfic example, we synthesize plasmonic layers that exhibit >2000x improvement in nonlinear optical properties, and 2D-superconductors combined with topological insulators as the building block of next generation “2D” topological superconductors. Confinement heteroepitaxy opens up avenues for enabling a virtual “legoland” of hybrid quantum materials.

4π and 8π dual Josephson effects induced by symmetry defects

In topological insulator edges, the duality between the Zeeman field orientation and the proximitized superconducting phase has been recently exploited to predict a magneto-Josephson effect with a 4$\pi$ periodicity. We revisit this latter Josephson effect in the light of this duality and show that the same 4$\pi$ quantum anomaly occurs when bridging two spinless Thouless pumps to a p-wave superconducting region that could be as small as a single and experimentally-relevant superconducting quantum dot - a point-like defect. This interpretation as a dual Josephson effect never requires the presence of Majorana modes but rather builds on the topological properties of adiabatic quantum pumps with Z topological invariants. It allows for the systematic construction of dual Josephson effects of arbitrary periodicity, such as 4$\pi$ and 8$\pi$, by using point-like defects whose symmetry differs from that of the pump, dubbed symmetry defects. Although adiabatic quantum pumps are typically discussed via mappings to two-dimensional geometries, we show that this phenomenology does not have any counterpart in conventional two-dimensional systems.

Disorder-Robust Entanglement Transport.

We study the disorder-perturbed transport of two noninteracting entangled particles in the absence of backscattering. This situation is, for instance, realized along edges of topological insulators. We find profoundly different responses to disorder-induced dephasing for the center-of-mass and relative coordinates: While a mirror symmetry protects even highly delocalized relative states when resonant with the symmetry condition, delocalizations in the center of mass [e.g., two-particle (N=2) N00N states] remain fully sensitive to disorder. We demonstrate the relevance of these differences to the example of interferometric entanglement detection. Our platform-independent analysis is based on the treatment of disorder-averaged quantum systems with quantum master equations.

Topological insulator ring with magnetic impurities

Topological insulators exhibit gapless edge or surface states that are topologically protected by time-reversal symmetry. However, several promising candidates for topologically insulating materials (such as Bi$_2$Se$_3$ and HgTe) contain spinful nuclei or other types of magnetic impurities that break time-reversal symmetry. We investigate the consequences of such impurities coupled to electronic edge states in a topological insulator quantum ring threaded by a magnetic flux. We use spin conservation and additional symmetry arguments to derive a universal formula for the spectrum of propagating edge modes in terms of the amplitude of transmission through the impurity. Our results apply for impurities of arbitrary spin. We show that there exists an energy regime in which the spectrum becomes nearly independent of the flux and significant spectral gaps form. We further analyze the electron-impurity entanglement entropy, finding that maximal entanglement occurs near the gaps in the spectrum. Our predictions can be investigated with quantum ring transport interference experiments or through spin-resolved STM measurements, providing a new approach to understand the role of impurities in topological insulator edge transport.

Odd-frequency superconducting pairing and subgap density of states at the edge of a two-dimensional topological insulator without magnetism

We investigate the emergence and consequences of odd-frequency spin-triplet s-wave pairing in superconducting hybrid junctions at the edge of a two-dimensional topological insulator without any magnetism. More specifically, we consider several different normal-superconductor hybrid systems at the topological insulator edge, where spin-singlet s-wave superconducting pairing is proximity-induced from an external conventional superconductor. We perform fully analytical calculations and show that odd-frequency mixed spin-triplet s-wave pairing arises due to the unique spin-momentum locking in the topological insulator edge state and the naturally non-constant pairing potential profile in hybrid systems. Importantly, we establish a one-to-one correspondence between the local density of states (LDOS) at low energies and the odd-frequency spin-triplet pairing in NS, NSN and SNS junctions along the topological insulator edge; at interfaces the enhancement in the LDOS can directly be attributed to the contribution of odd-frequency pairing. Furthermore, in SNS junctions we show that the emergence of the zero-energy LDOS peak at the superconducting phase $\phi=\pi$ is associated purely with odd-frequency pairing in the middle of the junction.

Edge absorption and pure spin current in a 2D topological insulator in the Volkov–Pankratov model

Light absorption due to transitions between the edge and two-dimensional (2D) states of a 2D topological insulator (TI) is considered in the Volkov–Pankratov model. It is shown that the transitions are allowed only for the in-plane electric field orthogonal to the TI edge. It is found that the absorption is accompanied by pure spin photocurrent along the TI edge. A possibility of spin current measurement using polarized luminescence from 2D TI quantum dots is discussed.

Linearity of the edge states energy spectrum in the 2D topological insulator

Linearity of the topological insulator edge state spectrum plays a crucial role for various transport phenomena. Previous studies found that this linearity exists near the spectrum crossing point, but did not determine how perfect the linearity is. The purpose of the present study is to answer this question in various edge states models. We examine Volkov and Pankratov (VP) model for the Dirac Hamiltonian and the model BHZ for the Bernevig, Hughes and Zhang (BHZ) Hamiltonian with zero boundary conditions. It is found that both models yield ideally linear edge states. In the BHZ1 model the linearity is conserved up to the spectrum ending points corresponding to the tangency of the edge spectrum with the boundary of 2D states. In contrast, the model BHZ2 with mixed boundary conditions for BHZ Hamiltonian and the 2D tight-binding (TB) model yield weak nonlinearity.

Current-induced switching of magnetic molecules on topological insulator surfaces

Electrical currents at the surface or edge of a topological insulator are intrinsically spin-polarized. We show that such surface/edge currents can be used to switch the orientation of a molecular magnet weakly coupled to the surface or edge of a topological insulator. For the edge of a two-dimensional topological insulator as well as for the surface of a three-dimensional topological insulator the application of a well-chosen surface/edge current can lead to a complete polarization of the molecule if the molecule's magnetic anisotropy axis is appropriately aligned with the current direction. For a generic orientation of the molecule a nonzero but incomplete polarization is obtained. We calculate the probability distribution of the magnetic states and the switching rates as a function of the applied current.

Regular and irregular dynamics of spin-polarized wavepackets in a mesoscopic quantum dot at the edge of topological insulator

The dynamics of Dirac-Weyl spin-polarized wavepackets driven by periodic electric field is considered for the electrons in a mesoscopic quantum dot formed at the edge of two-dimensional HgTe/CdTe topological insulator with Dirac-Weyl massless energy spectra, where the motion of carriers is less sensitive to disorder and impurity potentials. It was observed that the interplay of strongly coupled spin and charge degrees of freedom creates the regimes of irregular dynamics both in coordinate and spin channels. The border between the regular and irregular regimes determined by the strength and frequency of the driving field is found analytically within the quasiclassical approach by means of the Ince-Strutt diagram for Mathieu equation, and is supported by full quantum mechanical simulations of the driven dynamics. The investigation of quasienergy spectrum by Floquet approach reveals the presence of non-Poissonian level statistics which indicates the possibility of chaotic quantum dynamics and corresponds to the areas of parameters for irregular regimes within the quasiclassical approach. We found that the influence of weak disorder leads to partial suppression of the dynamical chaos. Our findings are of interest both for progress in a fundamental field of quantum chaotic dynamics and for further experimental and technological applications of spin-dependent phenomena in nanostructures based on topological insulators.

Aharonov-Bohm effect in a helical ring with long-range hopping: Effects of Rashba spin-orbit interaction and disorder

We study Aharonov-Bohm effect in a two-terminal helical ring with long-range hopping in presence of Rashba spin-orbit interaction. We explore how the spin polarization behavior changes depending on the applied magnetic flux and the incoming electron energy. The most interesting feature that we articulate in this system is that zero-energy crossings appear in the energy spectra at $\Phi=0$ and also at integer multiples of half-flux quantum values ($n \Phi_0/2$, $n$ being an integer) of the applied magnetic flux. We investigate the transport properties of the ring using Green's function formalism and find that the zero energy transmission peaks corresponding to those zero energy crossings vanish in presence of Rashba spin-orbit interaction. We also incorporate static random disorder in our system and show that the zero energy crossings and transmission peaks are not immune to disorder even in absence of Rashba spin-orbit interaction. The latter prevents the possibility of behaving these helical states in the ring like topological insulator edge states.

Effect of Impurities on the Josephson Current through Helical Metals: Exploiting a Neutrino Paradigm.

In this Letter we study the effect of time-reversal symmetric impurities on the Josephson supercurrent through two-dimensional helical metals such as on a topological insulator surface state. We show that, contrary to the usual superconducting-normal metal-superconducting junctions, the suppression of the supercurrent in the superconducting-helical metal-superconducting junction is mainly due to fluctuations of impurities in the junctions. Our results, which are a condensed matter realization of a part of the Mikheyev-Smirnov-Wolfenstein effect for neutrinos, show that the relationship between normal state conductance and the critical current of Josephson junctions is significantly modified for Josephson junctions on the surface of topological insulators. We also study the temperature dependence of the supercurrent and present a two fluid model which can explain some of the recent experimental results in Josephson junctions on the edge of topological insulators.

Two-dimensional topological insulator edge state backscattering by dephasing

To understand the seemingly absent temperature dependence in the conductance of two-dimensional topological insulator edge states, we perform a numerical study which identifies the quantitative influence of the combined effect of dephasing and elastic scattering in charge puddles close to the edges. We show that this mechanism may be responsible for the experimental signatures in HgTe/CdTe quantum wells if the puddles in the samples are large and weakly coupled to the sample edges. We propose experiments on artificial puddles which allow to verify this hypothesis and to extract the real dephasing time scale using our predictions. In addition, we present a new method to include the effect of dephasing in wave-packet-time-evolution algorithms.