Transport properties of topological insulators films and nanowires

The last several years have witnessed the rapid developments in the study and understanding of topological insulators. In this review, after a brief summary of the history of topological insulators, we focus on the recent progress made in transport experiments on topological insulator films and nanowires. Some quantum phenomena, including the weak antilocalization, the Aharonov-Bobm effect, and the Shubnikov-de Haas oscillations, observed in these nanostructures are described. In addition, the electronic transport evidence of the superconducting proximity effect as well as an anomalous resistance enhancement in topological insulator/superconductor hybrid structures is included.     

Photoemission Spectroscopic Evidence of Multiple Dirac Cones in Superconducting BaSn_3

Signatures of topological superconductivity(TSC) in superconducting materials with topological nontrivial states prompt intensive researches recently. Utilizing high-resolution angle-resolved photoemission spectroscopy and first-principles calculations, we demonstrate multiple Dirac fermions and surface states in superconductor BaSn_3 with a critical transition temperature of about 4.4 K. We predict and then unveil the existence of two pairs of type-Ⅰ topological Dirac fermions residing on the rotational axis. Type-Ⅱ Dirac fermions protected by screw axis are confirmed in the same compound. Further calculation for the spin helical texture of the observed surface states originating from the Dirac fermions gives an opportunity for realization of TSC in one single material.Hosting multiple Dirac fermions and topological surface states, the intrinsic superconductor BaSn_3 is expected to be a new platform for further investigation of topological quantum materials as well as TSC.     

Quantitative conditions for time evolution in terms of the von Neumann equation

The adiabatic theorem describes the time evolution of the pure state and gives an adiabatic approximate solution to the Schr ¨odinger equation by choosing a single eigenstate of the Hamiltonian as the initial state. In quantum systems, states are divided into pure states(unite vectors) and mixed states(density matrices, i.e., positive operators with trace one). Accordingly, mixed states have their own corresponding time evolution, which is described by the von Neumann equation. In this paper, we discuss the quantitative conditions for the time evolution of mixed states in terms of the von Neumann equation. First, we introduce the definitions for uniformly slowly evolving and δ-uniformly slowly evolving with respect to mixed states, then we present a necessary and sufficient condition for the Hamiltonian of the system to be uniformly slowly evolving and we obtain some upper bounds for the adiabatic approximate error. Lastly, we illustrate our results in an example.     

Magnetic Proximity Effect in an Antiferromagnetic Insulator/Topological Insulator Heterostructure with Sharp Interface

We report an experimental study of electron transport properties of MnSe/(Bi,Sb)_2Te_3 heterostructures,in which MnSe is an antiferromagnetic insulator,and(Bi,Sb)_2Te_3 is a three-dimensional topological insulator(TI).Strong magnetic proximity effect is manifested in the measurements of the Hall effect and longitudinal resistances.Our analysis shows that the gate voltage can substantially modify the anomalous Hall conductance,which exceeds 0.1 e~2/h at temperature T=1.6 K and magnetic field μ_0H=5 T,even though only the top TI surface is in proximity to MnSe.This work suggests that heterostructures based on antiferromagnetic insulators provide a promising platform for investigating a wide range of topological spintronic phenomena.     

Equivariant PT-symmetric real Chern insulators

It was understood that Chern insulators cannot be realized in the presence of PT symmetry.In this paper,we reveal a new class of PT-symmetric Chern insulators,which has internal degrees of freedom forming real representations of a symmetry group with a complex endomorphism field.As a generalization to the conventional 2n-dimensional Chern insulators with integer n≥1,these PT-symmetric Chern insulators have the n-th complex Chern number as their topological invariant,and have a Z classification given by the equivariant orthogonal K theory.Thus,in a fairly different sense,there exist ubiquitously Chern insulators with PT.symmetry.By generalizing the Thouless charge pump argument,we find that,for a PT-symmetric Chern insulator with Chern number v.there are equally many v flavors of coexisting left-and right-handed chiral modes.Chiral modes with opposite chirality are complex conjugates to each other as complex representations of the internal symmetry group,but are not isomorphic.For the physical dimensionality d=2,the PT-symmetric Chern insulators may be realized in artificial systems including photonic crystals and periodic mechanical systems.     

Non-Hermitian topological Anderson insulators

Non-Hermitian systems can exhibit exotic topological and localization properties.Here we elucidate the non-Hermitian effects on disordered topological systems using a nonreciprocal disordered Su-Schrieffer-Heeger model.We show that the non-Hermiticity can enhance the topological phase against disorders by increasing bulk gaps.Moreover,we uncover a topological phase which emerges under both moderate non-Hermiticity and disorders,and is characterized by localized insulating bulk states with a disorder-averaged winding number and zero-energy edge modes.Such topological phases induced by the combination of non-Hermiticity and disorders are dubbed non-Hermitian topological Anderson insulators.We reveal that the system has unique non-monotonous localization behavior and the topological transition is accompanied by an Anderson transition.These properties are general in other non-Hermitian models.     

Topological states in quasicrystals

With the rapid development of topological states in crystals, the study of topological states has been extended to quasicrystals in recent years. In this review, we summarize the recent progress of topological states in quasicrystals, particularly focusing on one-dimensional (1D) and 2D systems. We first give a brief introduction to quasicrystalline structures. Then, we discuss topological phases in 1D quasicrystals where the topological nature is attributed to the synthetic dimensions associated with the quasiperiodic order of quasicrystals. We further present the generalization of various types of crystalline topological states to 2D quasicrystals, where real-space expressions of corresponding topological invariants are introduced due to the lack of translational symmetry in quasicrystals. Finally, since quasicrystals possess forbidden symmetries in crystals such as five-fold and eight-fold rotation, we provide an overview of unique quasicrystalline symmetry-protected topological states without crystalline counterpart.     

Electrostatic field effects on three-dimensional topological insulators

Three-dimensional topological insulators are a new class of quantum matter which has interesting connections to nearly all main branches of condensed matter physics. In this article, we briefly review the advances in the field effect control of chemical potential in three-dimensional topological insulators. It is essential to the observation of many exotic quantum phenomena predicted to emerge from the topological insulators and their hybrid structures with other materials. We also describe various methods for probing the surface state transport. Some challenges in experimental study of electron transport in topological insulators will also be briefly discussed.     

Microscopic states of Kerr black holes from boundary-bulk correspondence

It was previously claimed by the author that black holes can be considered as topological insulators. Both black holes and topological insulators have boundary modes, and the boundary modes can be described by an effective BF theory. In this paper, the boundary modes on the horizons of black holes are analyzed using methods developed for topological insulators. BTZ black holes are analyzed first, and the results are found to be compatible with previous works. The results are then generalized to Kerr black holes, for which new results are obtained: dimensionless right-and left-temperatures can be defined and have well behavior in both the Schwarzschild limit a → 0 and the extremal limit a → M. Upon the Kerr/CFT correspondence, a central charge c = 12 Mr+ can be associated with an arbitrary Kerr black hole. Moreover, the microstates of the Kerr black hole can be identified with the quantum states of this scalar field. From this identification, the number of microstates of the Kerr black hole can be counted, yielding the Bekenstein-Hawking area law for the entropy.     

Finite size effects on the quantum spin Hall state in HgTe quantum wells under two different types of boundary conditions

The finite size effect in a two-dimensional topological insulator can induce an energy gap Eg in the spectrum of helical edge states for a strip of finite width.In a recent work,it has been found that when the spin–orbit coupling due to bulk-inversion asymmetry is taken into account,the energy gap Eg of the edge states features an oscillating exponential decay as a function of the strip width of the inverted Hg Te quantum well.In this paper,we investigate the effects of the interface between a topological insulator and a normal insulator on the finite size effect in the Hg Te quantum well by means of the numerical diagonalization method.Two different types of boundary conditions,i.e.,the symmetric and asymmetric geometries,are considered.It is found that due to the existence of the interface between topological insulator and normal insulator this oscillatory pattern on the exponential decay induced by bulk-inversion asymmetry is modulated by the width of normal insulator regions.With the variation of the width of normal insulator regions,the shift of the Dirac point of the edge states in the spectrum and the energy gap Eg closing point in the oscillatory pattern can occur.Additionally,the effect of the spin–orbit coupling due to structure-inversion asymmetry on the finite size effects is also investigated.     

拓扑绝缘体/超导体异质结中的近邻效应

拓扑超导体自身具有对量子退相干天然的免疫性以及可编织性,这使得它在现代量子计算领域中受到了越来越多的重视,并且成为了下一代计算技术中最有希望的候选者之一。由于拓扑超导态在固有拓扑超导体中相当罕见,因此,当前大部分实验上的工作主要集中在由 s 波超导体与拓扑绝缘体之间通过近邻效应所诱导的拓扑超导体上。本论文中,我们回顾了基于拓扑绝缘体/超导体异质结的拓扑超导体的研究进展。在理论上,Fu 和 Kane 提出,通过近邻效应将 s 波超导体的能隙引入到拓扑绝缘体,可以诱导出拓扑超导电性。在实验上,我们也回顾了一些不同体系中的拓扑超导近邻效应的研究进展。文章的第一部分,我们介绍了一些异质结,包括：三维拓扑绝缘体 Bi2Se3和 Bi2Se3 与 s 波超导体NbSe2 以及 d 波超导体 Bi2Sr2CaCu2O8+δ 的异质结,拓扑绝缘体 Sn1−xPbxTe 与 Pb 的异质结,二维拓扑绝缘体 WTe2 与NbSe2 的异质结。此外,还介绍了 TiBiSe2 在 Pb 上的拓扑绝缘近邻效应。另一部分中,我们对基于拓扑绝缘体的约瑟夫森结进行了回顾,包括著名的基于 Fu-Kane 体系的拓扑绝缘体约瑟夫森结,以及基于约瑟夫森结的超导量子干涉器件。     

Gapless interface states between topological insulators with opposite Dirac velocities

The Dirac cone on a surface of a topological insulator shows linear dispersion analogous to optics and its velocity depends on materials. We consider a junction of two topological insulators with different velocities, and calculate the reflectance and transmittance. We find that they reflect the backscattering-free nature of the helical surface states. When the two velocities have opposite signs, both transmission and reflection are prohibited for normal incidence, when a mirror symmetry normal to the junction is preserved. In this case we show that there necessarily exist gapless states at the interface between the two topological insulators. Their existence is protected by mirror symmetry, and they have characteristic dispersions depending on the symmetry of the system.     

Measurement of an exceptionally weak electron-phonon coupling on the surface of the topological insulator Bi2Se3 using angle-resolved photoemission spectroscopy

Gapless surface states on topological insulators are protected from elastic scattering on nonmagnetic impurities which makes them promising candidates for low-power electronic applications. However, for widespread applications, these states should have to remain coherent at ambient temperatures. Here, we studied temperature dependence of the electronic structure and the scattering rates on the surface of a model topological insulator, Bi2Se3, by high-resolution angle-resolved photoemission spectroscopy. We found an extremely weak broadening of the topological surface state with temperature and no anomalies in the state's dispersion, indicating exceptionally weak electron-phonon coupling. Our results demonstrate that the topological surface state is protected not only from elastic scattering on impurities, but also from scattering on low-energy phonons, suggesting that topological insulators could serve as a basis for room-temperature electronic devices.     

Experimental Realization of an Intrinsic Magnetic Topological Insulator

An intrinsic magnetic topological insulator(TI) is a stoichiometric magnetic compound possessing both inherent magnetic order and topological electronic states. Such a material can provide a shortcut to various novel topological quantum effects but remained elusive experimentally for a long time. Here we report the experimental realization of thin films of an intrinsic magnetic TI, MnBi_2Te_4, by alternate growth of a Bi_2Te_3 quintuple layer and a MnTe bilayer with molecular beam epitaxy. The material shows the archetypical Dirac surface states in angle-resolved photoemission spectroscopy and is demonstrated to be an antiferromagnetic topological insulator with ferromagnetic surfaces by magnetic and transport measurements as well as first-principles calculations. The unique magnetic and topological electronic structures and their interplays enable the material to embody rich quantum phases such as quantum anomalous Hall insulators and axion insulators at higher temperature and in a well-controlled way.     

Topological insulator as an optical modulator for pulsed solid‐state lasers

Topological insulators are states of quantum matter that have narrow topological nontrivial energy gaps and a large third‐order nonlinear optical response. The optical absorption of topological insulators can become saturated under strong excitation. In this work, with Bi₂Se₃ as an example, it was demonstrated that a topological insulator can modulate the operation of a bulk solid‐state laser by taking advantage of its saturable absorption. The result suggests that topological insulators are potentially attractive as broadband pulsed modulators for the generation of short and ultrashort pulses in bulk solid‐state lasers, in addition to other promising applications in physics and computing.     

拓扑绝缘基铁磁/铁磁超导隧道结的磁效应和塞曼效应(英文)

运用拓展的BTK理论研究了拓扑绝缘层上铁磁/铁磁超导隧道结的磁效应和塞曼效应,同时考虑了铁磁体和铁磁超导体之间的费米能级错配效应.研究发现:在该系统中塞曼效应和邻近效应可以共存;铁磁体和铁磁超导体之间的费米能级错配效应能够增强系统中发生在eV=Δ处的Andreev谐振散射过程和邻近效应.     

Disorder effects in topological states:Brief review of the recent developments

Disorder inevitably exists in realistic samples,manifesting itself in various exotic properties for the topological states.In this paper,we summarize and briefly review the work completed over the last few years,including our own,regarding recent developments in several topics about disorder effects in topological states.For weak disorder,the robustness of topological states is demonstrated,especially for both quantum spin Hall states with Z_2 = 1 and size induced nontrivial topological insulators with Z_2 = 0.For moderate disorder,by increasing the randomness of both the impurity distribution and the impurity induced potential,the topological insulator states can be created from normal metallic or insulating states.These phenomena and their mechanisms are summarized.For strong disorder,the disorder causes a metal-insulator transition.Due to their topological nature,the phase diagrams are much richer in topological state systems.Finally,the trends in these areas of disorder research are discussed.     

Electronic properties of SnTe-class topological crystalline insulator materials

The rise of topological insulators in recent years has broken new ground both in the conceptual cognition of condensed matter physics and the promising revolution of the electronic devices.It also stimulates the explorations of more topological states of matter.Topological crystalline insulator is a new topological phase,which combines the electronic topology and crystal symmetry together.In this article,we review the recent progress in the studies of SnTe-class topological crystalline insulator materials.Starting from the topological identifications in the aspects of the bulk topology,surface states calculations,and experimental observations,we present the electronic properties of topological crystalline insulators under various perturbations,including native defect,chemical doping,strain,and thickness-dependent confinement effects,and then discuss their unique quantum transport properties,such as valley-selective filtering and helicity-resolved functionalities for Dirac fermions.The rich properties and high tunability make SnTe-class materials promising candidates for novel quantum devices.