We demonstrate the existence of topological insulators in one dimension protected by mirror and time-reversal symmetries. They are characterized by a nontrivial $\mathbb{Z}_2$ topological invariant defined in terms of the "partial" polarizations, which we show to be quantized in presence of a 1D mirror point. The topological invariant determines the generic presence or absence of integer boundary charges at the mirror-symmetric boundaries of the system. We check our findings against spin-orbit coupled Aubry-André-Harper models that can be realized, e.g. in cold-atomic Fermi gases loaded in one-dimensional optical lattices or in density- and Rashba spin-orbit-modulated semiconductor nanowires. In this setup, in-gap end-mode Kramers doublets appearing in the topologically non-trivial state effectively constitute a double-quantum-dot with spin-orbit coupling.
Selective bulk-boundary correspondence in higher-order topological insulators with anticommuting mirror and chiral symmetries
Indiana University（印第安纳大学）；Department of Physics, Indiana University（印第安纳大学物理系）；Quantum Science and Engineering Center, Indiana University（印第安纳大学量子科学与工程中心）
We show that topological defects in quadrupole insulators do not host quantized fractional charges, contrary to what their Wannier representation indicates. In particular, we test the charge quantization hypothesis based on the Wannier representation of a parametric defect and a disclination. Against the expectations, we find that the local charge density decays as $\sim 1/r^2$ with distance, leading to a diverging defect charge. We identify sublattice symmetry and not higher order topology as the origin of the previously reported charge quantization.
We consider an interface between two strong time-reversal invariant topological insulators having surface states with opposite spin chirality, or equivalently, opposite mirror Chern number. We show that such an interface supports gapless modes that are protected by mirror symmetry. The interface states are investigated with a continuum model for the Bi2Se3 class of topological insulators that takes into account terms up to third order in the crystal momentum, which ensures that the model has the correct symmetry. The model parameters are obtained from ab initio calculations. Finally, we consid…
We study the multi-gap topology of the periodic spectra of Wilson loop operators (WLOs) in mirror symmetric insulators. We develop two topological invariants each associated with a mirror-invariant gap in the Wilson loop spectrum. We propose that both topological invariants in combination determine the general higher-order bulk-boundary correspondence in 2D mirror symmetric, boundary-obstructed topological insulators. Finally, we demonstrate that these new multi-gap topological invariants apply to anomalous cases beyond those captured by the nested Wilson loop, and we subsequently develop an u…
We discuss recent advances in the study of topological insulators protected by spatial symmetries by reviewing three representative, theoretical examples. In three dimensions, these states of matter are generally characterized by the presence of gapless boundary states at surfaces that respect the protecting spatial symmetry. We discuss the appearance of these topological states both in crystals with negligible spin-orbit coupling and a fourfold rotational symmetry, as well as in mirror-symmetric crystals with sizable spin-orbit interaction characterized by the so-called mirror Chern number. F…
We introduce the topological mirror excitonic insulator as a new type of interacting topological crystalline phase in one dimension. Its mirror-symmetry-protected topological properties are driven by exciton physics, and it manifests in the quantized bulk polarization and half-charge modes on the boundary. And the bosonization analysis is performed to demonstrate its robustness against strong correlation effects in one dimension. Besides, we also show that Rashba nanowires and Dirac semimetal nanowires could provide ideal experimental platforms to realize this new topological mirror excitonic …
Dynamical quantum phase transitions (DQPTs) are topologically characterized in quantum quench dynamics in topological systems. In this paper, we study Loschmidt amplitudes and DQPTs in quantum quenches in mirror-symmetric topological phases. Based on the topological classification of mirror-symmetric insulators, we show that mirror symmetry creates symmetry-protected DQPTs. If mirror symmetry is present, topologically robust DQPTs can occur in quantum quenches, even in high-dimensional time-reversal invariant systems. Then, we also show that symmetry-protected DQPTs occur in quenches in two-di…
Three-dimensional topological insulators protected by both the time reversal (TR) and mirror symmetries were recently predicted and observed. Two-dimensional materials featuring this property and their potential for device applications have been less explored. We find that in these systems, the spin-polarization of edge states can be controlled with an external electric field breaking the mirror symmetry. This symmetry requires that the spin-polarization is perpendicular to the mirror plane, therefore, the electric field induces spin-polarization components parallel to the mirror plane. Since …
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 condensed matter physics, symmetry profoundly governs the fundamentals of topological matter. The emergence of new topological phase is typically linked to the enrichment of symmetries. Different parity-time symmetry relations distinguish between spinless and spinful physical systems. In spinless systems, creating pseudo-spins can realize fragile topological phase but not break the time-reversal symmetry. Therefore, growing attentions were recently focused on the strong topological phase in spinless systems. Here we break the framework of crystallographic symmetry groups by utilizing the pr…
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…
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.
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…
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…
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…
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。
Bound states in the continuum (BICs) are counter-intuitive localized states with eigenvalues embedded in the continuum of extended states. Recently, nontrivial band topology is exploited to enrich the BIC physics, resulted in topological BICs (TBICs) with extraordinary robustness against perturbations or disorders. Here, we propose a simple but universal mirror-stacking approach to turn nontrivial bound states of any topological monolayer model into TBICs. Physically, the mirror-stacked bilayer Hamiltonian can be decoupled into two independent subspaces of opposite mirror parities, each of whi…
