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.     

Detection of Magnetic Gap in Topological Surface States of MnBi_2Te_4

Recently, intrinsic antiferromagnetic topological insulator MnBi_2Te_4 has drawn intense research interest and leads to plenty of significant progress in physics and materials science by hosting quantum anomalous Hall effect, axion insulator state, and other quantum phases. An essential ingredient to realize these quantum states is the magnetic gap in the topological surface states induced by the out-of-plane ferromagnetism on the surface of MnBi_2Te_4.However, the experimental observations of the surface gap remain controversial. Here, we report the observation of the surface gap via the point contact tunneling spectroscopy. In agreement with theoretical calculations, the gap size is around 50 me V, which vanishes as the sample becomes paramagnetic with increasing temperature.The magnetoresistance hysteresis is detected through the point contact junction on the sample surface with an out-of-plane magnetic field, substantiating the surface ferromagnetism. Furthermore, the non-zero transport spin polarization coming from the ferromagnetism is determined by the point contact Andreev reflection spectroscopy.Combining these results, the magnetism-induced gap in topological surface states of MnBi_2Te_4 is revealed.     

Edge solitons of topological insulators and fractionalized quasiparticles in two dimensions

An important characteristic of topological band insulators is the necessary presence of in-gap edge states on the sample boundary. We utilize this fact to show that when the boundary is reconnected with a twist, there are always zero-energy defect states. This provides a natural connection among novel defects in the two-dimensional p{x}+ip{y} superconductor, the Kitaev model, the fractional quantum Hall effect, and the one-dimensional domain wall of polyacetylene.     

AlO_x/LiF composite protection layer for Cr-doped(Bi,Sb)_2Te_3 quantum anomalous Hall films

We have realized robust quantum anomalous Hall samples by protecting Cr-doped(Bi,Sb)_2Te_3 topological insulator films with a combination of LiF and A1O_x capping layers.The AlO_x/LiF composite capping layer well keeps the quantum anomalous Hall states of Cr-doped(Bi,Sb)_2Te_3 films and effectively prevent them from degradation induced by ambient conditions.The progress is a key step towards the realization of the quantum phenomena in heterostructures and devices based on quantum anomalous Hall system.     

Electrically Tunable Wafer-Sized Three-Dimensional Topological Insulator Thin Films Grown by Magnetron Sputtering

Three-dimensional(3 D) topological insulators(TIs) are candidate materials for various electronic and spintronic devices due to their strong spin-orbit coupling and unique surface electronic structure.Rapid,low-cost preparation of large-area TI thin films compatible with conventional semiconductor technology is the key to the practical applications of TIs.Here we show that wafer-sized Bi_2 Te_3 family TI and magnetic TI films with decent quality and well-controlled composition and properties can be prepared on amorphous SiO_2/Si substrates by magnetron cosputtering.The SiO_2/Si substrates enable us to electrically tune(Bi_(1-x)Sb_x)_2 Te_3 and Cr-doped(Bi_(1-x)Sb_x)_2 Te_3 TI films between p-type and n-type behavior and thus study the phenomena associated with topological surface states,such as the quantum anomalous Hall effect(QAHE).This work significantly facilitates the fabrication of TI-based devices for electronic and spintronic applications.     

Quantum Anomalous Hall Multilayers Grown by Molecular Beam Epitaxy

Quantum anomalous Hall(QAH) effect is a quantum Hall effect that occurs without the need of external magnetic field. A system composed of multiple parallel QAH layers is an effective high Chern number QAH insulator and the key to the applications of the dissipationless chiral edge channels in low energy consumption electronics. Such a QAH multilayer can also be engineered into other exotic topological phases such as a magnetic Weyl semimetal with only one pair of Weyl points. This work reports the first experimental realization of QAH multilayers in the superlattices composed of magnetically doped(Bi,Sb)_2Te_3 topological insulator and Cd Se normal insulator layers grown by molecular beam epitaxy. The obtained multilayer samples show quantized Hall resistance h/N_e~2, where h is Planck's constant, e is the elementary charge and N is the number of the magnetic topological insulator layers, resembling a high Chern number QAH insulator. The QAH multilayers provide an excellent platform to study various topological states of matter.     

Effects of electric and magnetic fields on electronic states and transport of a Hall bar

We study the edge-state band and transport property for a HgTe/CdTe quantum well Hall bar under the combined coupling of a transverse electric field and a perpendicular magnetic field. It is demonstrated that a weak magnetic field can protect one of the two edge states, open or enlarge a gap of the other edge state in the Hall bar. However, an appropriate electric field can remove the gap, restoring the quantum spin Hall effect. Using the scattering matrix method, we study the electronic transport of the system. We find that the electric field can not only make the switch from pure spin-up to spin-down current, but also open or close the edge-state channels in a narrow Hall bar under a weak magnetic field, which provides us with a new way to construct a topological insulator-based spin switch and charge switch.     

三维拓扑绝缘体antidot阵列结构中的磁致输运研究

利用聚焦离子束刻蚀技术在拓扑绝缘体Bi_2Se_3薄膜中刻蚀了纳米尺度的反点(antidot)阵列,并对制作的三个器件进行了系统的电学输运测量研究.低温下,所有器件中都观察到明显的弱反局域化效应.通过对弱反局域化效应的分析,发现器件一(Dev-1,不含有antidot阵列)和器件二(Dev-2,含有周期较大的antidot阵列)是始终由一个导电通道主导的量子输运系统,但在器件三(Dev-3,含有周期较小的antidot阵列)中能明确观察到较低温度下存在两个独立的导电通道,而在较高温度下Dev-3表现为由一个导电通道主导的量子输运系统.     

Emergent Z_2 topological invariant and robust helical edge states in two-dimensional topological metals

In this work, we study the effects of disorder on topological metals that support a pair of helical edge modes deeply embedded inside the gapless bulk states. Strikingly, we predict that a quantum spin Hall(QSH) phase can be obtained from such topological metals without opening a global band gap. To be specific, disorder can lead to a pair of robust helical edge states which is protected by an emergent Z_2 topological invariant, giving rise to a quantized conductance plateau in transport measurements. These results are instructive for solving puzzles in various transport experiments on QSH materials that are intrinsically metallic. This work also will inspire experimental realization of the QSH effect in disordered topological metals.     

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.     

Rashba自旋轨道耦合下square-octagon晶格的拓扑相变

本文研究了各向同性square-octagon晶格在内禀自旋轨道耦合、Rashba自旋轨道耦合和交换场作用下的拓扑相变,同时引入陈数和自旋陈数对系统进行拓扑分类.系统在自旋轨道耦合和交换场的影响下会出现许多拓扑非平庸态,包括时间反演对称破缺的量子自旋霍尔态和量子反常霍尔态.特别的是,在时间反演对称破缺的量子自旋霍尔效应中,无能隙螺旋边缘态依然能够完好存在.调节交换场或者填充因子的大小会导致系统发生从时间反演对称破缺的量子自旋霍尔态到自旋过滤的量子反常霍尔态的拓扑相变.边缘态能谱和自旋谱的性质与陈数和自旋陈数的拓扑刻画完全一致.这些研究成果为自旋量子操控提供了一个有趣的途径.     

Topology of a <Superscript>3</Superscript>He-A Film on a Corrugated Graphene Substrate

A thin film of superfluid ³He on a corrugated graphene substrate represents topological matter with a smooth disorder. It is possible that the atomically smooth disorder produced by the corrugated graphene does not destroy the superfluidity even in a very thin film, where the system can be considered as quasi two-dimensional topological material. This will allow us to study the effect of disorder on different classes of the 2 + 1 topological materials: the chiral ³He-A with intrinsic quantum Hall effect and the time reversal invariant planar phase with intrinsic spin quantum Hall effect. In the limit of smooth disorder, the system can be considered as a Chern mosaic, i.e., a collection of domains with different values of Chern numbers. In this limit, the quantization of the Hall conductance is determined by the percolated domain, while the density of the fermionic states is determined by the edge modes on the boundaries of the finite domains. This system can be useful for the general consideration of disorder in the topological matter.     

Modification of the Hybridization Gap by Twisted Stacking of Quintuple Layers in a Three-Dimensional Topological Insulator Thin Film

Twisting the stacking of layered materials leads to rich new physics. A three-dimensional topological insulator film hosts two-dimensional gapless Dirac electrons on top and bottom surfaces, which, when the film is below some critical thickness, will hybridize and open a gap in the surface state structure. The hybridization gap can be tuned by various parameters such as film thickness and inversion symmetry, according to the literature. The three-dimensional strong topological insulator Bi(Sb)Se(Te) family has layered structures composed of quintuple layers(QLs) stacked together by van der Waals interaction. Here we successfully grow twistedly stacked Sb_2Te_3 QLs and investigate the effect of twist angels on the hybridization gaps below the thickness limit. It is found that the hybridization gap can be tuned for films of three QLs, which may lead to quantum spin Hall states.Signatures of gap-closing are found in 3-QL films. The successful in situ application of this approach opens a new route to search for exotic physics in topological insulators.     

Topological insulators in magnetic fields: quantum Hall effect and edge channels with a nonquantized θ term

We investigate how a magnetic field induces one-dimensional edge channels when the two-dimensional surface states of three-dimensional topological insulators become gapped. The Hall effect, measured by contacting those channels, remains quantized even in situations where the θ term in the bulk and the associated surface Hall conductivities, σ(xy)(S), are not quantized due to the breaking of time-reversal symmetry. The quantization arises as the θ term changes by ±2πn along a loop around n edge channels. Model calculations show how an interplay of orbital and Zeeman effects leads to quantum Hall transitions, where channels get redistributed along the edges of the crystal. The network of edges opens new possibilities to investigate the coupling of edge channels.     

Current correlations in quantum spin Hall insulators

We consider a four-terminal setup of a two-dimensional topological insulator (quantum spin Hall insulator) with local tunneling between the upper and lower edges. The edge modes are modeled as helical Luttinger liquids and the electron-electron interactions are taken into account exactly. Using perturbation theory in the tunneling, we derive the cumulant generating function for the interedge current. We show that different possible transport channels give rise to different signatures in the current noise and current cross correlations, which could be exploited in experiments to elucidate the interplay between electron-electron interactions and the helical nature of the edge states.     

Topological phase transition in anisotropic square-octagon lattice with spin–orbit coupling and exchange field

We investigate the topological phase transitions in an anisotropic square-octagon lattice in the presence of spin–orbit coupling and exchange field. On the basis of the Chern number and spin Chern number, we find a number of topologically distinct phases with tuning the exchange field, including time-reversal-symmetry-broken quantum spin Hall phases, quantum anomalous Hall phases and a topologically trivial phase. Particularly, we observe a coexistent state of both the quantum spin Hall effect and quantum anomalous Hall effect. Besides, by adjusting the exchange filed, we find the phase transition from time-reversal-symmetry-broken quantum spin Hall phase to spin-imbalanced and spin-polarized quantum anomalous Hall phases, providing an opportunity for quantum spin manipulation. The bulk band gap closes when topological phase transitions occur between different topological phases. Furthermore, the energy and spin spectra of the edge states corresponding to different topological phases are consistent with the topological characterization based on the Chern and spin Chern numbers.     

声子晶体中的多重拓扑相

研究了圆环型波导依照蜂窝结构排列的声子晶体系统中的拓扑相变.利用晶格结构的点群对称性实现赝自旋,并在圆环中引入旋转气流来打破时间反演对称性.通过紧束缚近似模型计算的解析结果表明,没有引入气流时,调节几何参数,系统存在普通绝缘体和量子自旋霍尔效应绝缘体两个相;引入气流后,可以实现新的时间反演对称性破缺的量子自旋霍尔效应相,而增大气流强度,则可以实现量子反常霍尔效应相.这三个拓扑相可以通过自旋陈数来分类.通过有限元软件模拟了多个系统中边界态的传播,发现不同于量子自旋霍尔效应相,量子反常霍尔相系统的表面只支持一种自旋的边界态,并且它无需时间反演对称性保护.     

Weyl semimetal in a topological insulator multilayer

We propose a simple realization of the three-dimensional (3D) Weyl semimetal phase, utilizing a multilayer structure, composed of identical thin films of a magnetically doped 3D topological insulator, separated by ordinary-insulator spacer layers. We show that the phase diagram of this system contains a Weyl semimetal phase of the simplest possible kind, with only two Dirac nodes of opposite chirality, separated in momentum space, in its band structure. This Weyl semimetal has a finite anomalous Hall conductivity and chiral edge states and occurs as an intermediate phase between an ordinary insulator and a 3D quantum anomalous Hall insulator. We find that the Weyl semimetal has a nonzero dc conductivity at zero temperature, but Drude weight vanishing as T(2), and is thus an unusual metallic phase, characterized by a finite anomalous Hall conductivity and topologically protected edge states.