Electron transport in magnetic-field-induced quasi-one-dimensional electron systems in semiconductor nanowhiskers

Many-body effects on tunneling of electrons in semiconductor nanowhiskers are investigated in a magnetic quantum limit. We consider the system with which bulk and edge states coexist. We show that interaction parameters of edge states are much smaller than those of bulk states and the tunneling conductance of edge states hardly depends on temperature and the singular behavior of tunneling conductance of bulk states can be observed.     

Spin edge states in two-dimensional electron systems

We consider the spin edge states, induced by the combined effect of spin-orbit interaction and hard-wall confining potential, in a two-dimensional electron system exposed to a perpendicular quantizing magnetic field. We derive an exact analytical formula for the dispersion relations of spin edge states and analyze their energy spectrum, velocity, and average transverse position. It is shown that by removing the spin degeneracy, spin-orbit interaction splits the spin edge states not only in the energy but also induces their spatial separation. It is revealed that at low magnetic fields, due to the Stark splitting of the spin-resolved edge states, the high-energy bands exhibit anti-crossings. This results in an additional structure in the behavior of the velocity of current-carrying edge states.     

Edge excitons in a 2D topological insulator in a magnetic field

Exciton edge states and the microwave edge exciton absorption of a 2D topological insulator subject to the in-plane magnetic field are studied. The magnetic field forms a narrow gap in electron edge states that allows the existence of edge exciton. The exciton binding energy is found to be much smaller than the energy of a 1D Coulomb state. Phototransitions exist on the exciton states with even numbers, while odd exciton states are dark.     

Effective spin dephasing mechanism in confined two-dimensional topological insulators

A Kramers pair of helical edge states in quantum spin Hall effect (QSHE) is robust against normal dephasing but not robust to spin dephasing. In our work, we provide an effective spin dephasing mechanism in the puddles of two-dimensional (2D) QSHE, which is simulated as quantum dots modeled by 2D massive Dirac Hamiltonian. We demonstrate that the spin dephasing effect can originate from the combination of the Rashba spin-orbit coupling and electron-phonon interaction, which gives rise to inelastic backscattering in edge states within the topological insulator quantum dots, although the time-reversal symmetry is preserved throughout. Finally, we discuss the tunneling between extended helical edge states and local edge states in the QSH quantum dots, which leads to backscattering in the extended edge states. These results can explain the more robust edge transport in InAs/GaSb QSH systems.     

Circular photogalvanic effect caused by the transitions between edge and 2D states in a 2D topological insulator

The electron absorption and the edge photocurrent of a 2D topological insulator are studied for transitions between edge states to 2D states. The circular polarized light is found to produce the edge photocurrent, the direction of which is determined by light polarization and edge orientation. It is shown that the edge-state current is found to exceed the 2D current owing to the topological protection of the edge states.     

自旋轨道耦合Su-Schrieffer-Heeger原子链系统的电子输运特性

在Su-Schrieffer-Heeger (SSH)原子链中,电子在胞内和胞间的跳跃依赖于其自旋时,即SSH原子链存在自旋轨道耦合作用时,存在不同缠绕数的非平庸拓扑边缘态.如何探测自旋轨道耦合SSH原子链不同缠绕数的边缘态是一个重要问题.本文在紧束缚近似下研究了自旋轨道耦合SSH原子链的非平庸拓扑边缘态性质及其零能附近的电子输运特性.研究发现四重和二重简并边缘态的缠绕数分别为2和1;并且仅当源极入射电子的自旋被极化(铁磁电极)时,自旋轨道耦合SSH原子链在零能附近的电子输运特性才能反映其边缘态的能谱特性.尤其是,随着自旋轨道耦合SSH原子链与左、右导线之间的耦合强度由弱到强改变,对于缠绕数为2的四重简并边缘态,入射电子在零能附近的透射峰数目将从4个变为0;而对于缠绕数为1的二重简并边缘态情形,其透射峰数目将从2个变为0.因此,在源极为铁磁电极的情形下,通过观察自旋轨道耦合SSH原子链在零能附近电子共振透射峰的数目随着其与左、右导线之间耦合强度的变化,来探测其不同缠绕数的边缘态.上述结果为基于电子输运特性探测自旋轨道耦合SSH原子链不同拓扑性质的边缘态提供了一种可选择的理论方案.     

Photoinduced anisotropic edge states and signatures of nonequilibrium spin polarization in silicene nanoribbons

Most topological phase transitions are accompanied by the emergence of surface/edge states with spin dependence. Usually, the quantized Hall conductivity cannot characterize the anisotropic transports and spin dependence of topological states. Here, we study the intricate topological phase transition and the anisotropic behavior of edge states in silicene nanoribbon submitted to an electric field or/and a light irradiation. It is interesting to find that a circularly polarized light can induce a type-II quantum anomaly Hall phase, which is manifested as the high Chern number and the strong anisotropic edge states. Besides the measurement of the quantized Hall conductivity, we further propose to probe these topological phase transitions and the anisotropy of edge states by measuring the current-induced nonequilibrium spin polarization. It is found that the spin polarization exhibits more signatures about the behavior of surface/edge states, beyond the quantized Hall conductivity, especially for spin-dependent transports with different velocities.     

Evolution of individual quantum Hall edge states in the presence of disorder

By using the Bloch eigenmode matching approach, we numerically study the evolution of individual quantum Hall edge states with respect to disorder. As demonstrated by the two-parameter renormalization group flow of the Hall and Thouless conductances, quantum Hall edge states with high Chern number n are completely different from that of the n = 1 case. Two categories of individual edge modes are evaluated in a quantum Hall system with high Chern number. Edge states from the lowest Landau level have similar eigenfunctions that are well localized at the system edge and independent of the Fermi energy. On the other hand, at fixed Fermi energy, the edge state from higher Landau levels exhibit larger expansion, which results in less stable quantum Hall states at high Fermi energies. By presenting the local current density distribution, the effect of disorder on eigenmode-resolved edge states is distinctly demonstrated.     

Charge redistribution between cyclotron-resolved edge states at high imbalance

We use a quasi-Corbino sample geometry with independent contacts to different edge states in the quantum Hall effect regime to investigate a charge redistribution between cyclotron-split edge states at high imbalance. We also modify the Büttiker formalism by introducing local transport characteristics in it and use this modified Büttiker picture to describe the experimental results. We find that charge transfer between cyclotron-split edge states at high imbalance can be described by a single parameter, which is a transferred between edge states portion of the available for transfer part of the electrochemical potential imbalance. This parameter is found to be independent of the particular sample characteristics, describing fundamental properties of the interedge-state scattering. From the experiment we obtain it in the dependence on the voltage imbalance between edge states and propose a qualitative explanation to the experimental findings.     

Spin effects in edge transport in two-dimensional topological insulators

Investigations of topological insulators, which are two- and three-dimensional systems with a gap in the bulk spectrum and topologically protected gapless edge states, are of considerable fundamental interest at present. The experiments confirming the presence of the edge states in two-dimensional systems with inverted bands and problems of determining the nature of such states in these experiments are reviewed. Special attention is focused on spin-sensitive experiments since the topological edge states have a nontrivial spin structure.     

Electronic structure of rectangular HgTe quantum dots

We theoretically investigate the single- and few-electron ground-states properties of HgTe topological insulator quantum dots with rectangular hard-wall confining potential using configuration interaction method. For the case of single electron, the edge states is robust against the deformation from a square quantum dot to a rectangular ones, in contrast to the bulk states, the energy gap of the QDs increased due to the coupling of the opposite edge states; for the case of few electrons, the electrons first fill the edge states in the bulk band gap and the addition energy exhibit universal even-odd oscillation due to the shape-independent two-fold degeneracy of the edge states. The size of this edge shell can be controlled by tuning the dot size, shape or the bulk band gap via lateral or vertical electric gating respectively of the HgTe quantum dot.     

Edge states enhanced by long-range hopping: An analytical study

We analyze the behavior of edge states in long-range(LR) interacting systems. In terms of lattice model Hamiltonian with the LR coupling, we determine analytically the condition of existence of edge states within the transfer matrix method(TMM). The expressions we obtain are general and hold for any choice of the LR hopping. The reason why edge states can appear is the transfer matrix in the bulk different from that in the boundary layers. Our predictions are in good agreement with numerical results by exact diagonalization. Our result is helpful in solving novel edge states in oneand two-dimensional(2D) superconductors with LR hopping and pairing.     

Quantum transport signatures of non-trivial topological edge states in a ring-shaped Su–Schrieffer–Heeger double-chain system

In the ring-shaped Su–Schrieffer–Heeger(SSH)double-chain,the quantum interference between the two different electron tunneling paths of the upper and lower chains has an important influence on the electron transport properties of non-trivial topological edge states.Here,we have studied the electron transport signatures of non-trivial topological edge states in a ring-shaped SSH double-chain system based on the wave-guide theory and transfer-matrix method.In the ringshaped SSH double-chain with the upper chain being different from the lower one,it is demonstrated that the electron transmission probability displays the four and two resonance peaks associated with the non-trivial topological edge states in the weak and strong coupling regimes,respectively.Whereas in the case of the upper chain being the same as the lower one,the two transmission resonance peaks associated with the non-trivial topological edge states in the weak coupling regime are only found,and that in the strong coupling regime disappear that originated from the destructive interference between the two different electron tunneling paths of the upper and lower chains.Consequently,the variation of the number of transmission resonance peaks associated with the non-trivial topological edge states in the weak and strong coupling regimes suggests that an alternative scheme for detecting non-trivial topological edge states in the ring-shaped SSH doublechain system.     

磁场中的拓扑绝缘体边缘态性质

用数值方法研究了拓扑绝缘体薄膜体系在外加垂直磁场 作用下其边缘态的性质. 磁场的加入通过耦合k+eA, 即Peierls势替换关系和 该作用导致的Zeeman交换场体现在哈密顿量中. 考虑窄条圆环状结构的二维InAs/GaSb/AlSb薄膜量子阱材料, 当其处于拓扑非平庸状态, 即量子自旋霍尔态时, 会出现受时间反演对称性保护的两支简并边缘态, 而在垂直磁场的作用下, 时间反演对称性被破坏, 这时能带将形成一条条的朗道能级, 原来简并的两支边缘态也会分开到朗道能级谱线的两侧, 从电子态密度的空间分布情况则可以看到边缘态分别局域在材料的两个边界. 随着磁场的增大, 位于同一边界上的不同 自旋极化的边缘态将出现分离: 一支仍然局域在边缘, 另一支则随外加磁场的增加而有逐渐演化到材料内部的趋势. 文中还计算了同一边界上的两支边缘态之间的散射, 结果表明由于两个边缘态在空间发生分离, 相互之间的散射被很大的压制, 得到了其散射随磁场增加没有明显变化的结论, 所以磁场并不会增强散射过程, 也没有破坏体拓扑材料的性质, 说明了量子自旋霍尔态在没有时间反演对称的情况下也可以有较强的稳定性.     

Quench dynamics of edge states in 2-D topological insulator ribbons

We study the dynamics of edge states of the two dimensional BHZ Hamiltonian in a ribbon geometry following a sudden quench to the quantum critical point separating the topological insulator phase from the trivial insulator phase. The effective edge state Hamiltonian is a collection of decoupled qubit-like two-level systems which get coupled to bulk states following the quench. We notice a pronounced collapse and revival of the Lochschmidt echo for low-energy edge states illustrating the oscillation of the state between the two edges. We also observe a similar collapse and revival in the spin Hall current carried by these edge states, leading to a persistence of its time-averaged value.     

Controllable simulation of topological phases and edge states with quantum walk

We simulate various topological phenomena in condense matter, such as formation of different topological phases, boundary and edge states, through two types of quantum walk with step-dependent coins. Particularly, we show that one-dimensional quantum walk with step-dependent coin simulates all types of topological phases in BDI family, as well as all types of boundary and edge states. In addition, we show that step-dependent coins provide the number of steps as a controlling factor over the simulations. In fact, with tuning number of steps, we can determine the occurrences of boundary, edge states and topological phases, their types and where they should be located. These two features make quantum walks versatile and highly controllable simulators of topological phases, boundary, edge states, and topological phase transitions. We also report on emergences of cell-like structures for simulated topological phenomena. Each cell contains all types of boundary (edge) states and topological phases of BDI family.     

Effect of edge vacancies on localized states in a semi-infinite zigzag graphene sheet

The effect of vacancies on the robustness of zero-energy edge electronic states in zigzag-type graphene layer is studied at different concentrations and distributions of defects. All calculations are performed by using the Green’s function method and the tight-binding approximation. It is found that the arrangement of defects plays a crucial role in the destruction of the edge states. We have specified a critical distance between edge vacancies when their mutual influence becomes significant and affects markedly the density of electronic states at graphene edge.     

Edge electron states for quasi-one-dimensional organic conductors in the magnetic-field-induced spin-density-wave phases

We develop a microscopic picture of the electron states localized at the edges perpendicular to the chains in the Bechgaard salts in the quantum Hall regime. In a magnetic-field-induced spin-density-wave state characterized by an integer N, there exist N branches of chiral gapless edge excitations. Localization length is much longer and velocity much lower for these states than for the edge states parallel to the chains. We calculate the contribution of these states to the specific heat and propose a time-of-flight experiment to probe the propagating edge modes directly.     

Exact confined eigenstates in one-dimensional finite periodic systems with arbitrary symmetric basis

A set of eigenenergy equations for complete confinement of N periodic one-dimensional system with arbitrary symmetric potential in each cell is presented. Exact eigenenergies and their eigenfunctions are solved analytically. We find different solutions on the band edge states comparing early results solved by conventional methods. Our results show that higher band edge state of each bandgap is dependent on the confined length, but lower band edge state is independent of the length. Moreover, wavefunctions for lower band edge states are Bloch waves but those for other eigenstates, including higher band edge states, do not obey Bloch waves.     

Majorana edge states in interacting one-dimensional systems

We show that one-dimensional electron systems in the proximity of a superconductor that support Majorana edge states are extremely susceptible to electron-electron interactions. Strong interactions generically destroy the induced superconducting gap that stabilizes the Majorana edge states. For weak interactions, the renormalization of the gap is nonuniversal and allows for a regime in which the Majorana edge states persist. We present strategies of how this regime can be reached.