Coexistence of giant Rashba spin splitting and quantum spin Hall effect in H–Pb–F

Rashba spin splitting(RSS)and quantum spin Hall effect(QSHE)have attracted enormous interest due to their great significance in the application of spintronics.In this work,we theoretically proposed a new two-dimensional(2D)material H–Pb–F with coexistence of giant RSS and quantum spin Hall effec by using the ab initio calculations.Our results show that H–Pb–F possesses giant RSS(1.21 eV·A)and the RSS can be tuned up to 4.16 e V·A by in-plane biaxial strain,which is a huge value among 2D materials.Furthermore,we also noticed that H–Pb–F is a 2D topological insulator(TI)duo to the strong spin–orbit coupling(SOC)interaction,and the large topological gap is up to 1.35 e V,which is large enough for for the observation of topological edge states at room temperature.The coexistence of giant RSS and quantum spin Hall effect greatly broadens the potential application of H–Pb–F in the field of spintronic devices.

Quantum spin Hall and quantum valley Hall effects in trilayer graphene and their topological structures

The present study pertains to the trilayer graphene in the presence of spin orbit coupling to probe the quantum spin/valley Hall effect. The spin Chern-number Cs for energy-bands of trilayer graphene having the essence of intrinsic spin-orbit coupling is analytically calculated. We find that for each valley and spin, Cs is three times larger in trilayer graphene as compared to single layer graphene. Since the spin Chern-number corresponds to the number of edge states, consequently the trilayer graphene has edge states, three times more in comparison to single layer graphene. We also study the trilayer graphene in the presence of both electric-field and intrinsic spin-orbit coupling and investigate that the trilayer graphene goes through a phase transition from a quantum spin Hall state to a quantum valley Hall state when the strength of the electric field exceeds the intrinsic spin coupling strength. The robustness of the associated topological bulk-state of the trilayer graphene is evaluated by adding various perturbations such as Rashba spin-orbit （RSO） interaction αR, and exchange-magnetization M. In addition, we consider a theoretical model, where only one of the outer layers in trilayer graphene has the essence of intrinsic spin-orbit coupling, while the other two layers have zero intrinsic spin-orbit coupling. Although the first Chern number is non-zero for individual valleys of trilayer graphene in this model, however, we find that the system cannot be regarded as a topological insulator because the system as a whole is not gaped.

Spin Chern numbers and time-reversal-symmetry-broken quantum spin Hall effect

The quantum spin Hall （QSH） effect is considered to be unstable to perturbations violating the time-reversal （TR） symmetry. We review some recent developments in the search of the QSH effect in the absence of the TR symmetry. The possibility to realize a robust QSH effect by artificial removal of the TR symmetry of the edge states is explored. As a useful tool to characterize topological phases without the TR symmetry, the spin-Chern number theory is introduced.

The robustness of the quantum spin Hall effect to the thickness fluctuation in HgTe quantum wells

The quantum spin Hall effect （QSHE） was first realized in HgTe quantum wells （QWs）, which remain the only known two-dimensional topological insulator so far. In this paper, we have systematically studied the effect of the thickness fluctuation of HgTe QWs on the QSHE. We start with the case of constant mass with random distributions, and reveal that the disordered system can be well described by a virtual uniform QW with an effective mass when the number of components is small. When the number is infinite and corresponds to the real fluctuation, we find that the QSHE is not only robust, but also can be generated by relatively strong fluctuation. Our results imply that the thickness fluctuation does not cause backscattering, and the QSHE is robust to it.

Quantum spin Hall effect in a square-lattice model under a uniform magnetic field

We study a toy square-lattice model under a uniform magnetic field. Using the Landauer Biittiker fornmla, we calculate the transport properties of the system on a two-terminal, a four-terminal and a six-terminM device. W＇e find that the quantum spin Hall （QSH） effect appears ill energy ranges where the spin-up and spin-down subsystems have different filling factors. We also study the robustness of the resulting QSH effect and find that it is robust when the Fermi levels of both spin subsystems are far away from the energy plateaus but is fragile when the Fermi level of any spin subsystem is near the energy plateaus. These results provide an example of the QSH effect with a physical origin other than time-reversal （TR） preserving spin-orbit coupling （SOC）.

Discovery of Two-Dimensional Quantum Spin Hall Effect in Triangular Transition-Metal Carbides

Though the quantum spin Hall effect（QSHE） in two-dimensional（2 D） crystals has been widely explored, the experimental realization of quantum transport properties is only limited to HgTe/CdTe or InAs/GaSb quantum wells. Here we employ a tight-binding model on the basis of d（z^2）, d（xy）, and d（x^2-y^2） orbitals to propose QSHE in the triangular lattice, which are driven by a crossing of electronic bands at the Γ point. Remarkably, 2 D oxidized Mxenes W2 M2 C3 are ideal materials with nontrivial gap of 0.12 eV, facilitating room-temperature observations in experiments. We also find that the nontrivially topological properties of these materials are sensitive to the cooperative effect of the electron correlation and spin-orbit coupling. Due to the feasible exfoliation from its 3 D MAX phase, our work paves a new direction towards realizing QSHE with low dissipation.

On the mystery of the absence of a spin-orbit gap in scanning tunneling microscopy spectra of germanene

Germanene,the germanium analogue of graphene,shares many properties with its carbon counterpart.Both materials are two-dimensional materials that host Dirac fermions.There are,however,also a few important differences between these two materials:(1)graphene has a planar honeycomb lattice,whereas germanene’s honeycomb lattice is buckled and(2)the spin-orbit gap in germanene is predicted to be about three orders of magnitude larger than the spin-orbit gap in graphene(24 meV for germanene versus 20μeV for graphene).Surprisingly,scanning tunneling spectra recorded on germanene layers synthesized on different substrates do not show any sign of the presence of a spin-orbit gap.To date the exact origin of the absence of this spin-orbit gap in the scanning tunneling spectra of germanene has remained a mystery.In this work we show that the absence of the spin-orbit gap can be explained by germanene’s exceptionally low work function of only 3.8 eV.The difference in work function between germanene and the scanning tunneling microscopy tip(the work functions of most commonly used STM tips are in the range of 4.5 to 5.5 eV)gives rise to an electric field in the tunnel junction.This electric field results in a strong suppression of the size of the spin-orbit gap.

Quantum spin Hall effect in inverted InAs/GaSb quantum wells

We review the recent experimental progress towards observing quantum spin Hall effect in inverted InAs/GaSb quantum wells （QWs）. Low temperature transport measurements in the hybridization gap show bulk conductivity of a non-trivial origin, while the length and width dependence of con- ductance in this regime show strong evidence for the existence of helical edge modes proposed by Liu et al. [Phys. Rev. Lett., 2008, 100： 236601]. Surprisingly, edge modes persist in spite of compa- rable bulk conduction and show only weak dependence on magnetic field. We elucidate that seeming independence of edge on bulk transport comes due to the disparity in Fermi-wave vectors between the bulk and the edge, leading to a total internal reflection of the edge modes.

Topological insulator nanostructures and devices

Topological insulators＇ properties and their potential device applications are reviewed. We also explain why topologi- cal insulator （TI） nanostructnres are an important avenue for research and discuss some methods by which TI nanostructures are produced and characterized. The rapid development of high-quality TI nanostructures provides an ideal platform to ex- ploit salient physical phenomena that have been theoretically predicted but not yet experimentally realized.

Electronic structures and topological properties of TeSe_(2) monolayers

The successfully experimental fabrication of two-dimensional Te monolayer films[Phys.Rev.Lett.119106101(2017)]has promoted the researches on the group-VI monolayer materials.In this work,the electronic structures and topological properties of a group-VI binary compound of TeSe_(2) monolayers are studied based on the density functional theory and Wannier function method.Three types of structures,namely,a-TeSe_(2),b-TeSe_(2),and g-TeSe_(2),are proposed for the TeSe_(2) monolayer among which the a-TeSe_(2) is found being the most stable.All the three structures are semiconductors with indirect band gaps.Very interestingly,the g-TeSe_(2) monolayer becomes a quantum spin Hall(QSH)insulator with a global nontrivial energy gap of 0.14 eV when a 3.5%compressive strain is applied.The opening of the global band gap is understood by the competition between the decrease of the local band dispersion and the weakening of the interactions between the Se px,py orbitals and Te px,py orbitals during the process.Our work realizes topological states in the group-VI monolayers and promotes the potential applications of the materials in spintronics and quantum computations.

Progress on 2D topological insulators and potential applications in electronic devices

Two-dimensional topological insulators(2DTIs)have attracted increasing attention during the past few years.New 2DTIs with increasing larger spin-orbit coupling(SOC)gaps have been predicted by theoretical calculations and some of them have been synthesized experimentally.In this review,the 2DTIs,ranging from single element graphene-like materials to bi-elemental transition metal chalcogenides(TMDs)and to multi-elemental materials,with different thicknesses,structures,and phases,have been summarized and discussed.The topological properties(especially the quantum spin Hall effect and Dirac fermion feature)and potential applications have been summarized.This review also points out the challenge and opportunities for future 2DTI study,especially on the device applications based on the topological properties.

Classification of Topological Insulators with Time-Reversal and Inversion Symmetry

In this paper, we find that topological insulators with time-reversal symmetry and inversion symmetry featuring two-dimensional quantum spin Hall （QSH） state can be divided into 16 classes, which are characterized by four Z2 topological variables ζk =0, 1 at four points with high symmetry in the Brillouin zone. We obtain the corresponding edge states for each one of these sixteen classes of QSHs. In addition, it is predicted that massless fermionic excitations appear at the quantum phase transition between different QSH states. In the end, we also briefly discuss the threedimensional case.

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 Hamiltouian. 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.

量子自旋霍尔绝缘体Bi_(4)Br_(4)体与边缘的可区分的光学性质研究

量子自旋霍尔绝缘体拥有具有带隙的体态和无能隙的一维拓扑边缘态.然而,由于拓扑边缘态局域在纳米尺度,所以很难用光学手段直接观测并区分体态和边缘态,这就限制了对拓扑边缘态独特的光学特性和光电响应等方面的研究和应用.Bi_(4)Br_(4)体材料的台阶存在一维非平庸的边缘态,多个台阶累加的效应使得通过较为宏观的光学和光电分析手段来研究一维边缘态成为可能.该工作利用中远红外显微吸收光谱和泵浦探测光谱,对比研究了Bi_(4)Br_(4)体和边缘的光学响应行为.研究发现Bi_(4)Br_(4)的边缘在小于带隙(约0.22 eV)的波段存在明显的强于体内的红外吸收,且该吸收呈现较强的各向异性.室温下的红外泵浦探测首次观察到边缘处载流子激发态超长的弛豫时间(1.5 ns),该激发态载流子寿命要比体内载流子寿命长两个量级.该工作证实体态和拓扑边缘态具有明显不同的光学和光电响应行为,为未来设计新型红外探测器提供了材料和物理基础.