Photoexcitation in two-dimensional topological insulators

One of the most fascinating challenges in Physics is the realization of an electron-based counterpart of quantum optics, which requires the capability to generate and control single electron wave packets. The edge states of quantum spin Hall (QSH) systems, i.e., two-dimensional (2D) topological insulators realized in HgTe/CdTe and InAs/GaSb quantum wells, may turn the tide in the field, as they do not require the magnetic field that limits the implementations based on quantum Hall effect. However, the band structure of these topological states, described by a massless Dirac fermion Hamiltonian, prevents electron photoexcitation via the customary vertical electric dipole transitions of conventional optoelectronics. So far, proposals to overcome this problem are based on magnetic dipole transitions induced via Zeeman coupling by circularly polarised radiation, and are limited by the g-factor. Alternatively, optical transitions can be induced from the edge states to the bulk states, which are not topologically protected though.Here we show that an electric pulse, localized in space and/or time and applied at a QSH edge, can photoexcite electron wavepackets by intra-branch electrical transitions, without invoking the bulk states or the Zeeman coupling. Such wavepackets are spin-polarised and propagate in opposite directions, with a density profile that is independent of the initial equilibrium temperature and that does not exhibit dispersion, as a result of the linearity of the spectrum and of the chiral anomaly characterising massless Dirac electrons. We also investigate the photoexcited energy distribution and show how, under appropriate circumstances, minimal excitations (Levitons) are generated. Furthermore, we show that the presence of a Rashba spin–orbit coupling can be exploited to tailor the shape of photoexcited wavepackets. Possible experimental realizations are also discussed.     

Spin transport in antiferromagnetic insulators

Electrical spin, which is the key element of spintronics, has been regarded as a powerful substitute for the electrical charge in the next generation of information technology, in which spin plays the role of the carrier of information and/or energy in a similar way to the electrical charge in electronics. Spin-transport phenomena in different materials are central topics of spintronics. Unlike electrical charge, spin transport does not depend on electron motion, particularly spin can be transported in insulators without accompanying Joule heating. Therefore, insulators are considered to be ideal materials for spin conductors, in which magnetic insulators are the most compelling systems. Recently, we experimentally studied and theoretically discussed spin transport in various antiferromagnetic systems and identified spin susceptibility and the Néel vector as the most important factors for spin transport in antiferromagnetic systems. Herein, we summarize our experimental results, physical nature, and puzzles unknown. Further challenges and potential applications are also discussed.     

Magnetic quantum ring in two-dimensional topological insulators

The quantum properties of topological insulator magnetic quantum rings formed by inhomogeneous magnetic fields are investigated using a series expansion method for the modified Dirac equation. Cycloid-like and snake-like magnetic edge states are respectively found in the bulk gap for the normal and inverted magnetic field profiles. The energy spectra, current densities and classical trajectories of the magnetic edge states are discussed in detail. The bulk band inversion is found to manifest itself through the angular momentum transition in the ground state for the cycloid-like states and the resonance tunneling effect for the snake-like states.     

Dephasing effects in topological insulators

Topological insulators, a class of typical topological materials in both two dimensions and three dimensions,are insulating in bulk and metallic at surface. The spin-momentum locked surface states and peculiar transport properties exhibit promising potential applications on quantum devices, which generate extensive interest in the last decade. Dephasing is the process of the loss of phase coherence, which inevitably exists in a realistic sample. In this review, we focus on recent progress in dephasing effects on the topological insulators. In general, there are two types of dephasing processes: normal dephasing and spin dephasing. In two-dimensional topological insulators, the phenomenologically numerical investigation shows that the longitudinal resistance plateaus is robust against normal dephasing but fragile with spin dephasing. Several microscopic mechanisms of spin dephasing are then discussed. In three-dimensional topological insulators, the helical surface states exhibit a helical spin texture due to the spin-momentum locking mechanism. Thus, normal dephasing has close connection to spin dephasing in this case, and gives rise to anomalous “gap-like” feature. Dephasing effects on properties of helical surface states are investigated.     

Photogalvanic effects in topological insulators

We discuss optical absorption in topological insulators and study possible photoelectric effects theoretically. We found that absorption of circularly polarized electromagnetic waves in two-dimensional topological insulators results in electric current in the conducting 1D edge channels, the direction of the current being determined by the light polarization. We suggest two ways of inducing such a current: due to magnetic dipole electron transitions stimulated by irradiation of frequency below the bulk energy gap, and due to electric dipole transitions in the bulk at frequencies larger than the energy gap with subsequent capture of the photogenerated carriers on conducting edge states.     

Efficiency of electrical manipulation in two-dimensional topological insulators

We investigate the efficiency of electrical manipulation in a two-dimensional topological insulator by inspecting the electronic states of a lateral electrical potential superlattice in the system. The spatial distribution of the electron density in the system can be tuned by changing the strength of the externally applied lateral electrical superlattice potential. This provides us the information about how efficiently one can manipulate the electron motion inside a two-dimensional topo- logical insulator. Such information is important in designing electronic devices, e.g., an electric field effect transistor made of the topological insulator. The electronic states under various conditions are examined carefully. It is found that the dispersion of the mini-band and the electron distribution in the potential well region both display an oscillatory behavior as the potential strength of the lateral superlattice increases. The probability of finding an electron in the potential well region can be larger or smaller than the average as the potential strength varies. These features can be attributed to the coupled multiple-band nature of the topological insulator. In addition, it is also found that these behaviors are not sensitive to the gap parameter of the two-dimensional topological insulator model. Our study suggests that the electron density manipulation via electrical gating in a two-dimensional topological insulator is less effective and more delicate than that in a traditional single-band semiconductor.     

二维有机拓扑绝缘体的研究进展

新材料的发现促进了科学与技术的进步.拓扑绝缘体是近期材料领域新的研究热点,相关研究的进一步深入,不仅加深了人们对材料物理性质的理解,也为其在自旋电子学和量子计算机等领域的潜在应用提供了有价值的参考.近年来,理论工作预测了一系列由金属和有机物构筑的二维有机拓扑绝缘体,本文主要介绍六角对称的金属有机晶格与Kagome金属有机晶格两类典型的二维有机拓扑绝缘体的研究进展,其中重点介绍了理论预测的氰基配位二维本征有机拓扑绝缘体.除了理论计算方面的工作,还简要介绍了关于二维有机拓扑绝缘体材料合成方面的实验工作.二维有机拓扑绝缘体的理论与实验研究不仅拓展了拓扑绝缘体的研究体系,还为寻找新的拓扑绝缘体材料提供了思路.     

Appearance and disappearance of edge states in topological insulators

We investigate the relationship between spin Chern numbers and edge state properties in general situations, where the time-reversal symmetry may be broken. As an example, we consider a thin film of three-dimensional topological insulators sandwiched between two ferromagnetic insulators with an antiparallel magnetization configuration. A topological quantum spin Hall phase with quantized spin Chern numbers C _± =  ±1, and a trivial insulator with C _± = 0 are found in different parameter regions. With tuning parameters, the quantum phase transition between the two phases can occur through closing of the spin spectrum gap rather than energy gap. It is further shown that for a junction between samples with different parameters, appearance of edge states at the interface is always related to the mismatch of spin Chern numbers, independent of symmetries.     

二维拓扑绝缘体退相干效应研究

拓扑绝缘体是当前凝聚态物理研究的热点.退相干效应对该体系的影响的研究不仅有重要的理论意义,而且也是实现未来量子器件的不可或缺的前期工作.文章作者从理论上研究了退相干对二维拓扑绝缘体特别是量子自旋霍尔效应的影响.研究结果表明,作为量子自旋霍尔效应的标志的量子化纵向电阻平台对不破坏自旋记忆的退相干效应（普通退相干）不敏感,但却对破坏自旋记忆的退相干效应（自旋退相干）非常敏感.因此,该量子化平台只能在尺寸小于自旋退相干长度的介观样品中存在,从而解释了量子自旋霍尔效应实验中所观测到的结果(见Science ,20     

二维拓扑绝缘体退相干效应研究

拓扑绝缘体是当前凝聚态物理研究的热点.退相干效应对该体系的影响的研究不仅有重要的理论意义,而且也是实现未来量子器件的不可或缺的前期工作.文章作者从理论上研究了退相干对二维拓扑绝缘体特别是量子自旋霍尔效应的影响.研究结果表明,作为量子自旋霍尔效应的标志的量子化纵向电阻平台对不破坏自旋记忆的退相干效应(普通退相干)不敏感,但却对破坏自旋记忆的退相干效应(自旋退相干)非常敏感.因此,该量子化平台只能在尺寸小于自旋退相干长度的介观样品中存在,从而解释了量子自旋霍尔效应实验中所观测到的结果(见Science,2007,318:766).同时,文章作者还定义了一个新的物理量,即自旋霍尔电阻,并发现该自旋霍尔电阻也有量子化平台.特别是该量子化平台对两种类型的退相干都不敏感.这说明在宏观样品中也能观测到自旋霍尔电阻的量子化平台,因此更能全面地反映量子自旋霍尔效应的拓扑特性.     

Thermoelectric effects and topological insulators

The recent discovery of topological insulators(TIs) offers new opportunities for the development of thermoelectrics,because many TIs(like Bi_2Te_3) are excellent thermoelectric(TE) materials.In this review,we will first describe the general TE properties of TIs and show that the coexistence of the bulk and boundary states in TIs introduces unusual TE properties,including strong size effects and an anomalous Seebeck effect.Importantly,the TE figure of merit zT of TIs is no longer an intrinsic property,but depends strongly on the geometric size.The geometric parameters of twodimensional TIs can be tuned to enhance zT to be significantly greater than 1.Then a few proof-of-principle experiments on three-dimensional TIs will be discussed,which observed unconventional TE phenomena that are closely related to the topological nature of the materials.However,current experiments indicate that the metallic surface states,if their advantage of high mobility is not fully utilized,would be detrimental to TE performance.Finally,we provide an outlook for future work on topological materials,which offers great possibilities to discover exotic TE effects and may lead to significant breakthroughs in improving zT.     

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.     

Electron transport properties of three-dimensional topological insulators

We review experimental advances in the study of the electron transport in three-dimensional topological insulators with emphasis on experiments that attempted to identify the surface transport. Recent results on transport properties of topological insulator thin films will be discussed in the context of weak antilocalization and electron-electron interactions. Current status of gate-voltage control of the chemical potential in topological insulators will also be described.     

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.     

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.     

Pseudo topological insulators

We predict pseudo topological insulators that have been previously overlooked. We determine some conditions under which robust pseudo topological edge states appear and illustrate our idea on the Su–Schrieffer–Heeger (SSH) model with extra chiral symmetry breaking potentials. We discuss that pseudo topological insulating phase transition occurs without band gap closing.     

On ballistic transport in topological insulators with the structure of borders

The symmetry nature of the appearance of specific surface (edge) states at the boundaries of low-dimension structures with the symmetry of ribbons (borders) invariant with respect to time reversal is discussed. Symmetry reasons for the stability of such states against the elastic scattering from nonmagnetic impurities have been revealed.     

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.     

Spin gauge fields: From Berry phase to topological spin transport and Hall effects

The paper examines the emergence of gauge fields during the evolution of a particle with a spin that is described by a matrix Hamiltonian with n different eigenvalues. It is shown that by introducing a spin gauge field a particle with a spin can be described as a spin multiplet of scalar particles situated in a non-Abelian pure gauge (forceless) field U (n). As the result, one can create a theory of particle evolution that is gauge-invariant with regards to the group Uⁿ (1). Due to this, in the adiabatic (Abelian) approximation the spin gauge field is an analogue of n electromagnetic fields U (1) on the extended phase space of the particle. These fields are force ones, and the forces of their action enter the particle motion equations that are derived in the paper in the general form. The motion equations describe the topological spin transport, pumping, and splitting. The Berry phase is represented in this theory analogously to the Dirac phase of a particle in an electromagnetic field. Due to the analogy with the electromagnetic field, the theory becomes natural in the four-dimensional form. Besides the general theory, the article considers a number of important particular examples, both known and new.     

Model characterization of gapless edge modes of topological insulators using intermediate Brillouin-zone functions

We characterize gapless edge modes in translation invariant topological insulators. We show that the edge mode spectrum is a continuous deformation of the spectrum of a certain gluing function defining the occupied state bundle over the Brillouin zone. Topologically nontrivial gluing functions, corresponding to nontrivial bundles, then yield edge modes exhibiting spectral flow. We illustrate our results for the case of chiral edge states in two-dimensional Chern insulators, as well as helical edges in quantum spin Hall states.