A three-dimensional weak topological insulator (WTI), being equivalent to stacked layers of two-dimensional quantum spin-Hall insulators, accommodates massless Dirac electrons on its side surface. A notable feature of WTIs is that surface states typically consist of two Dirac cones in the reciprocal space. We study the Landau quantization of Dirac electrons of WTIs in a perpendicular magnetic field. It is shown that when the magnetic length $l_B$ is much larger than the interlayer distance $a$, surface electrons are quantized into Landau levels according to the ordinary quantization rule for Dirac electrons. It is also shown that, with decreasing $l_B$ toward $a$, each Landau level and its spin state become modulated in a nontrivial manner. We demonstrate that this is attributed to the mixing of two Dirac cones induced by the discreteness of the layered structure.
We investigate the ballistic zitterbewegung dynamics and the Landau-Zener tunneling between edge and bulk states of wave packets in two-dimensional topological insulators. In bulk, we use the Ehrenfest theorem to show that an external in-plane electric field not only drifts the packet longitudinally, but also induces a transverse finite side-jump for both trivial and topological regimes. For finite ribbons of width $W$, we show that the Landau-Zener tunneling between bulk and edge states vanishes for large $W$ as their electric field-induced coupling decays with $W^{-3/2}$. This is demonstrate…
The effect of magnetic field on an ultrathin magnetic topological insulator film with structural inversion asymmetry is investigated. We introduce the phase diagram, calculate the Landau-level spectrum analytically and simulate the transport behavior in Landauer-Büttiker formalism. The quantum anomalous Hall phase will survive increasing magnetic field. Due to the two spin polarized zero modes of Landau levels a nontrivial phase similar with quantum spin Hall effect can be induced by magnetic field which is protected by structural inversion symmetry. Some exotic longitudinal and Hall resistanc…
The intrinsic magnetic topological insulators, Mn(Bi1-xSbx)2Te4, in their spin-aligned strong field configuration have been identified as a Weyl semimetal with single pair of Weyl nodes1-4. A direct consequence of the Weyl state is the layer-dependent Chern number (C) in thin film quantization. Previous reports in MnBi2Te4 thin films revealed the higher C states in the spin alignment by either increasing the film thickness5 or controlling chemical potential into electron doping6-8. A clear picture of the higher Chern states is still missing as the situation is complicated by the emerging of su…
A key feature of the topological surface state under a magnetic field is the presence of the zeroth Landau level at the zero energy. Nonetheless, it has been challenging to probe the zeroth Landau level due to large electron-hole puddles smearing its energy landscape. Here, by developing ultra-low-carrier density topological insulator Sb$_2$Te$_3$ films, we were able to reach an extreme quantum limit of the topological surface state and uncover a hidden phase at the zeroth Landau level. First, we discovered an unexpected quantum-Hall-to-insulator-transition near the zeroth Landau level. Then, …
The lifetime of electrons on edge states of a two-dimensional topological insulator against the background of an allowed two-dimensional band has been determined. It has been shown that this time in the case of scattering on Coulomb impurities can be significantly larger than the mean free time of two-dimensional electrons. As a result, the conductivity of the metallic two-dimensional topological insulator strip can be determined primarily by edge states.
In this paper we investigate quasiparticles in graphene-based topological insulator with a wedge disclination in the presence of a uniform magnetic field. In particular, we consider a massive spinless model. The Landau levels are analytically found for the described system. We show that the Landau levels are lifted for a specific range of the parameter ν. In addition, we also show that, for appropriate parameter values, one finds gapless and gapped states.
Eigenenergies of a non-Hermitian system without parity-time symmetry are complex in general. Here, we show that the chiral boundary states of higher-dimensional (two-dimensional and three-dimensional) non-Hermitian topological insulators without parity-time symmetry can be Hermitian with real eigenenergies under certain conditions. Our approach allows one to construct Hermitian chiral edge and hinge states from non-Hermitian two-dimensional Chern insulators and three-dimensional second-order topological insulators, respectively. Such Hermitian chiral boundary channels have perfect transmission…
We propose a different route to time-reversal invariant Weyl semimetals employing multilayer heterostructures comprising ordinary "trivial" insulators and nontrivial insulators with \textit{pairs} of protected Dirac cones on the surface. We consider both the case of weak topological insualtors, where surface Dirac cones are pinned to time-reversal invariant momenta, and of topological crystalline insulators with unpinned surface Dirac cones. For both realizations we explain phenomenologically how the proposed construction leads to the emergence of a Weyl semimetal phase. We further formulate e…
The Landauer "residual resistivity dipole" is a well-known concept in electron transport through a disordered medium. It is formed when a defect/scatterer reflects an impinging electron causing negative charges to build up on one side of the scatterer and positive charges on the other. This results in the formation of a microscopic electric dipole that affects the resistivity of the medium. Here, we show that an equivalent entity forms in spin polarized electron transport through the surface of a disordered topological insulator (TI). When electrons reflect from a scatterer on the TI surface, …
Lecture-notes: introducing and discussing basics on axion electrodynamics with application in the calculation of the images generated by an electric (or a magnetic) charge located close to an interface ordinary insulator-topological insulator
We study spin conductivity of the surface states in a thin film of a topological insulator with Kubo formulas. Hybridization between the different sides of the film opens a gap at the Dirac point. We found that in the gapped region spin conductivity remains finite. In the gapless region near the band gap spin conductivity is enhanced. These findings make a thin film of a topological insulator as a promising material for spintronic applications.
In this paper we consider modification of electronic properties of graphene-based topological insulator in the presence of wedge disclination and magnetic field by adopting the Kane-Mele model with intrinsic spin-orbit coupling. Using the properly defined Dirac-Weyl equation for this system, an exact solution for the Landau levels is obtained. The influence of the topological defect on the evolution of Landau levels is discussed.
We study a non-Hermitian non-Abelian topological insulator preserving $PT$ symmetry, where the non-Hermitian term represents nonreciprocal hoppings. As it increases, a spontaneous $PT$ symmetry breaking transition occurs in the perfect-flat band model from a real-line-gap topological insulator into an imaginary-line-gap topological insulator. By introducing a band bending term, we realize two phase transitions, where a metallic phase emerges between the above two topological insulator phases. We discuss an electric-circuit realization of non-Hermitian non-Abelian topological insulators. We fin…
We investigate scattering of the topological surface state of a three-dimensional time-reversal invariant topological insulator when graphene is deposited on the topological-insulator surface. Specifically, we consider the (111) surface of a Bi$_2$Se$_3$-like topological insulator. We present a low-energy model for the bulk graphene-topological insulator heterostructure and we calculate the transmission probability at zigzag and armchair edges of the deposited graphene, and the conductance through graphene nanoribbon barriers and show that its features can be understood from antiresonances in …
The electronic bands are classified according to their topology. We compute the connection and curvature for the electronic bands and show that the physical properties are determined by topological invariants which are equivalent to the existence of the zero modes. We apply this method to the Topological Insulators and Topogical Superconductors.
Topological phases, including the conventional first-order and higher-order topological insulators and semimetals, have emerged as a thriving topic in the fields of condensed-matter physics and material science. Usually, a topological insulator is characterized by a fixed order topological invariant and exhibits associated bulk-boundary correspondence. Here, we realize a new type of topological insulator in a bilayer phononic crystal, which hosts simultaneously the first-order and second-order topologies, referred here as the hybrid-order topological insulator. The one-dimensional gapless heli…
Thanks to its unique symmetry, the unidirectional spin Hall and Rashba-Edelstein magnetoresistance (USRMR) is of great fundamental and practical interest, particularly in the context of reading magnetization states in two-terminal spin-orbit torque switching memory and logic devices. Recent studies show that topological insulators could improve USRMR amplitude. However, the topological insulator device configurations studied so far in this context, namely ferromagnetic metal/topological insulator bilayers and magnetically doped topological insulators, suffer from current shunting by the metall…
We consider weak topological insulators with a twofold rotation symmetry around the dark direction, and show that these systems can be endowed with the topological crystalline structure of a higher-order topological insulator protected by rotation symmetry. These hybrid-order weak topological insulators display surface Dirac cones on all surfaces. Translational symmetry breaking perturbations gap the Dirac cones on the side surfaces leaving anomalous helical hinge modes behind. We also prove that the existence of this topological phase comes about due to a hidden crystalline topological invari…
Notion of square-root topological insulators have been recently generalized to higher-order topological insulators. In two-dimensional square-root higher-order topological insulators, emergence of in-gap corner states are inherited from the squared Hamiltonian which hosts higher-order topology. In this paper, we propose that the martini lattice model serves as a concrete example of higher-order topological insulators. Furthermore, we also propose a suquare-root higher-order topological insulator based on the martini model. Specifically, we propose that the honeycomb lattice model with two-site…
The search of novel topological phases, such as the quantum anomalous Hall insulator (QAHI) or the axion insulator, has motivated different schemes to introduce magnetism into topological insulators. One scheme is to introduce ferromagnetic dopants in topological insulators. However, it is generally challenging and requires carefully engineered growth/heterostructures or relatively low temperatures to observe the QAHI due to issues such as the added disorder with ferromagnetic dopants. Another promising scheme is using the magnetic proximity effect with a magnetic insulator to magnetize the to…
It has been proposed that adding disorder to a topologically trivial mercury telluride/cadmium telluride (HgTe/CdTe) quantum well can induce a transition to a topologically nontrivial state. The resulting state was termed topological Anderson insulator and was found in computer simulations of the Bernevig-Hughes-Zhang model. Here, we show that the topological Anderson insulator is a more universal phenomenon and also appears in the Kane-Mele model of topological insulators on a honeycomb lattice. We numerically investigate the interplay of the relevant parameters, and establish the parameter r…
The possible realization of dissipationless chiral edge current in a topological insulator / magnetic insulator heterostructure is based on the condition that the magnetic proximity exchange coupling at the interface is dominated by the Dirac surface states of the topological insulator. Here we report a polarized neutron reflectometry observation of Dirac electrons mediated magnetic proximity effect in a bulk-insulating topological insulator (Bi$_{0.2}$Sb$_{0.8}$)$_{2}$Te$_{3}$ / magnetic insulator EuS heterostructure. We are able to maximize the proximity induced magnetism by applying an elec…
We present a generalization of free fermionic topological insulators that are composed of topological subsystems of differing dimensionality. We specifically focus on topological subsystems of nonzero co-dimension are embedded within a trivial insulating environment. A general procedure is described to isolate and classify such embedded topological insulators and we present three representative examples in varying dimensions and symmetry classes. Moreover, we demonstrate with concrete examples that the presence of periodically embedded topological insulators in an otherwise trivially classifie…
We investigate a topological switch between second-order topological insulators (SOTIs) and topological crystalline insulators (TCIs). Both the SOTI and the TCI are protected by the mirror and inversion symmetries, for which we define the bulk topological numbers of the same type. We take examples of square nanodisks on the square lattice and hexagonal nanodisks on the triangular lattice. When inplane magnetic field is introduced parallel to one of the helical edges, the system becomes a TCI. The conductance along the edge is 1 in the unit of the conductance quantum $e^2/h$. As the inplane fie…
Fluctuations of Hamiltonian eigenfunctions, measured by the inverse participation ratio (IPR), turn out to characterize topological-band insulator transitions occurring in 2D Dirac materials like silicene, which is isostructural with graphene but with a strong spin-orbit interaction. Using monotonic properties of the IPR, as a function of a perpendicular electric field (which provides a tunable band gap), we define topological-like quantum numbers that take different values in the topological-insulator and band-insulator phases.
Second-order topological insulators are crystalline insulators with a gapped bulk and gapped crystalline boundaries, but topologically protected gapless states at the intersection of two boundaries. Without further spatial symmetries, five of the ten Altland-Zirnbauer symmetry classes allow for the existence of such second-order topological insulators in two and three dimensions. We show that reflection symmetry can be employed to systematically generate examples of second-order topological insulators and superconductors, although the topologically protected states at corners (in two dimension…
We introduce a coupled-layer construction to describe three-dimensional topological crystalline insulators protected by reflection symmetry. Our approach uses stacks of weakly-coupled two-dimensional Chern insulators to produce topological crystalline insulators in one higher dimension, with tunable number and location of surface Dirac cones. As an application of our formalism, we turn to a simplified model of topological crystalline insulator SnTe, showing that its protected surface states can be described using the coupled layer construction.
Transport Properties of Topological Insulators Films and Nanowires
近几年来，人们对拓扑绝缘体的研究和认识发展迅速。本文在简要总结了拓扑绝缘体的发展历史后，重点介绍了拓扑绝缘体薄膜和纳米线输运实验的最新进展。一些量子现象，包括弱反局域化，Aharonov玻姆效应和Shubnikov de Haas振荡，在这些纳米结构中观察到的描述。此外，超导邻近效应的电子输运证据，以及在拓扑绝缘体/超导体混合结构的异常电阻增强包括在内。
The disorder effects on higher-order topological phases in periodic systems have attracted much attention. However, in aperiodic systems, such as quasicrystalline systems, the interplay between disorder and higher-order topology is still unclear. In this paper, we investigate the effects of disorder on two types of second-order topological insulators, including a quasicrystalline quadrupole insulator and a modified quantum spin Hall insulator, in a two-dimensional Amman-Beenker tiling quasicrystalline lattice. We demonstrate that the higher-order topological insulators are robust against weak …
Tunneling magnetoresistance devices based on topological insulators: Ferromagnet/insulator/topological-insulator junctions employing Bi$_{2}$Se$_{3}$
本文从理论上研究了三维拓扑绝缘体Bi $_{2}$ Se $_{3}$的隧穿磁电阻（TMR）器件。基于Bi $_{2}$ Se $_{3}$的现实紧束缚模型进行理论计算。我们研究了利用Bi $_{2}$ Se $_{3}$的表面态的三维器件，以及利用薄Bi $_{2}$ Se $_{3}$条的边缘态的二维器件。我们证明了Bi $_{2}$ Se $_{3}$的材料性质允许在室温下的TMR比为1000%的量级。分析公式推导出，允许在这些设备中实现的TMR比的快速估计。该装置可用于测量自旋极化的拓扑表面状态作为替代自旋ARPES。与基于磁性隧道结的TMR器件不同，本器件避免使用其磁化需要被钉扎的第二铁磁电极。
In three-dimensional topological insulators (TIs), the nontrivial topology in their electronic bands casts a gapless state on their solid surfaces, using which dissipationless TI edge devices based on the quantum anomalous Hall (QAH) effect and quantum Hall (QH) effect have been demonstrated. Practical TI devices present a pair of parallel-transport topological surface states (TSSs) on their top and bottom surfaces. However, due to the no-go theorem, the two TSSs always appear as a pair and are expected to quantize synchronously. Quantized transport of a separate Dirac channel is still desirab…
We review low and high field magnetotransport in 80 nm-thick strained HgTe, a material that belongs to the class of strong three-dimensional topological insulators. Utilizing a top gate, the Fermi level can be tuned from the valence band via the Dirac surface states into the conduction band and allows studying Landau quantization in situations where different species of charge carriers contribute to magnetotransport. Landau fan charts, mapping the conductivity $ σ_{xx}(V_g, B) $ in the whole magnetic field - gate voltage range, can be divided into six areas, depending on the state of the parti…
