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.

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.

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.

Quantum spin Hall effect in inverted InAs/GaSb quantum wells

我们向在转换 InAs/GaSb 量井(QW ) 观察量旋转霍尔效果考察最近的试验性的进步。在杂交差距的低温度运输大小显示出重要起源的体积电导率，当长度和在这政体的传导力的宽度依赖证明为螺旋状的边模式的存在的充分证据由刘等求婚了时。[Phys。加快。Lett， 2008， 100：236601 ] 。令人惊讶地，尽管有可比较的体积传导，边模式坚持并且在磁场上显示出仅仅弱的依赖。我们阐明体积运输上的边的那表面上的独立在在体积和边之间的费密波浪向量由于不同来，导致边模式的全部的内部思考。

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 HgTe 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 HgTe 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.

Finite size effects on helical edge states in HgTe quantum wells with the spin orbit coupling due to bulk- and structure-inversion asymmetries

There is a quantum spin Hall state in the inverted HgTe quantum well, characterized by the topologically protected gapless helical edge states lying within the bulk gap. It has been found that for a strip of finite width, the edge states on the two sides can couple together to produce a gap in the spectrum. The phenomenon is called the finite size effect in quantum spin Hall systems. In this paper, we investigate the effects of the spin-orbit coupling due to bulk- and structure-inversion asymmetries on the finite size effect in the HgTe quantum well by means of the numerical diagonalization method. When the bulk-inversion asymmetry is taken into account, it is shown that the energy gap Eg of the edge states due to the finite size effect features an oscillating exponential decay as a function of the strip width of the HgTe quantum well. The origin of this oscillatory pattern on the exponential decay is explained. Furthermore, if the bulk- and structure-inversion asymmetries are considered simultaneously, the structure-inversion asymmetry will induce a shift of the energy gap Eg closing point. Finally, based on the roles of the bulk- and structure-inversion asymmetries on the finite size effects, a way to realize the quantum spin Hall field effect transistor is proposed.

Spin Polarization of Fractional Quantum Hall States with <i>ν</i><2

The spin polarization of a fractional quantum Hall state shows very interesting properties. The curve of polarization versus magnetic field has wide plateaus. The fractional quantum Hall effect is caused by the Coulomb interaction because the 2D electron system without the Coulomb interaction yields no energy gap at the fractional filling factor. Therefore, the wide plateau in the polarization curve is also caused by the Coulomb interaction. When the magnetic field is weak, some electrons have up-spins and the others down-spins. Therein the spin-exchange transition occurs between two electrons with up and down spins via the Coulomb interaction. Then the charge distribution before the transition is the same as one after the transition. So these two states have the same classical Coulomb energy. Accordingly, the partial Hamiltonian composed of the spin exchange interaction should be treated exactly. We have succeeded in diagonalizing the spin exchange interaction for the first and second nearest electron pairs. The theoretical results reproduce the wide plateaus very well. If the interval modulations between Landau orbitals are taken into the Hamiltonian, the total energy has the Peierls instability. We can diagonalize the Hamiltonian with the interval modulation. The results reproduce wide plateaus and small shoulders which are in good agreement with the experimental data.

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.

冷原子中的光致量子自旋Hall效应

讨论在冷原子体系中利用光致规范场模拟量子自旋霍尔效应.通过对6Li这样的多能级原子施加适当的激光脉冲,构造出具二重兼并的能量暗态(能量为零的本征态).类似于自旋二分量体系,可以分别定义2个暗态为自旋向上及自旋向下态.当原子在空间分布的激光场中运动时,其所感受到的有效自旋相关规范场将导致可观测的自旋霍尔电流.

Electronic structure of molecular beam epitaxy grown 1T’-MoTe2 film and strain effect

Atomically thin transition metal dichalcogenide films with distorted trigonal(1T') phase have been predicted to be candidates for realizing quantum spin Hall effect. Growth of 1T' film and experimental investigation of its electronic structure are critical. Here we report the electronic structure of 1T'-MoTe2 films grown by molecular beam epitaxy(MBE).Growth of the 1T'-MoTe2 film depends critically on the substrate temperature, and successful growth of the film is indicated by streaky stripes in the reflection high energy electron diffraction(RHEED) and sharp diffraction spots in the low energy electron diffraction(LEED). Angle-resolved photoemission spectroscopy(ARPES) measurements reveal a metallic behavior in the as-grown film with an overlap between the conduction and valence bands. First principles calculation suggests that a suitable tensile strain along the a-axis direction is needed to induce a gap to make it an insulator. Our work not only reports the electronic structure of MBE grown 1T'-MoTe2 films, but also provides insights for strain engineering to make it possible for quantum spin Hall effect.

Quantum anomalous Hall effect and giant Rashba spin-orbit splitting in graphene system co-doped with boron and 5d transition-metal atoms

Quantum anomalous Hall effect （QAHE） is a fundamental quantum transport phenomenon in con- densed matter physics. Until now, the QAHE has only been experimentally realized for Cr/V-doped （Bi, Sb）2We3 but at an extremely low observational temperature, thereby limiting its potential appli- cation in dissipationless quantum electronics. By employing first-principles calculations, we study the electronic structures of graphene co-doped with 5d transition metal and boron atoms based on a com- pensated n-p co-doping scheme. Our findings are as follows： i） The electrostatic attraction between the n- and p-type dopants effectively enhances the adsorption of metal adatoms and suppresses their undesirable clustering, ii） Hf-B and Os-B co-doped graphene systems can establish long-range ferro- magnetic order and open larger nontrivial band gaps because of the stronger spin-orbit coupling with the non-vanishing Berry curvatures to host the high-temperature QAHE. iii） The calculated Rashba splitting energies in Re-B and Pt-B co-doped graphene systems can reach up to 158 and 85 meV, re- spectively, which are several orders of magnitude higher than the reported intrinsic spin-orbit coupling strength.

Finite size effects on the helical edge states on the Lieb lattice

For a two-dimensional Lieb lattice,that is,a line-centered square lattice,the inclusion of the intrinsic spin–orbit（ISO）coupling opens a topologically nontrivial gap,and gives rise to the quantum spin Hall（QSH） effect characterized by two pairs of gapless helical edge states within the bulk gap.Generally,due to the finite size effect in QSH systems,the edge states on the two sides of a strip of finite width can couple together to open a gap in the spectrum.In this paper,we investigate the finite size effect of helical edge states on the Lieb lattice with ISO coupling under three different kinds of boundary conditions,i.e.,the straight,bearded and asymmetry edges.The spectrum and wave function of edge modes are derived analytically for a tight-binding model on the Lieb lattice.For a strip Lieb lattice with two straight edges,the ISO coupling induces the Dirac-like bulk states to localize at the edges to become the helical edge states with the same Dirac-like spectrum.Moreover,it is found that in the case with two straight edges the gapless Dirac-like spectrum remains unchanged with decreasing the width of the strip Lieb lattice,and no gap is opened in the edge band.It is concluded that the finite size effect of QSH states is absent in the case with the straight edges.However,in the other two cases with the bearded and asymmetry edges,the energy gap induced by the finite size effect is still opened with decreasing the width of the strip.It is also proposed that the edge band dispersion can be controlled by applying an on-site potential energy on the outermost atoms.

Two-dimensional transport and strong spin-orbit interaction in SrMnSb_2

We have carried out magneto-transport measurements for single crystal SrMnSb2. Clear Shubnikov-de Haas oscil- lations were resolved at relatively low magnetic field around 4 T, revealing a quasi-2D Fermi surface. We observed a development of quantized plateaus in Hall resistance （Rxy） at high pulsed fields up to 60 T. Due to the strong 2D confine- ment and layered properties of the samples, we interpreted the observation as bulk quantum Hall effect that is contributed by the parallel 2D conduction channels. Moreover, the spin degeneracy was lifted leading to Landau level splitting. The presence of anisotropic g factor and the formation of the oscillation beating pattern reveal a strong spin-orbit interaction in the SrMnSb2 system.

α-T_(3)晶格中量子反常霍尔效应研究

量子反常霍尔绝缘体具有与普通绝缘体一样的体带隙,但在其边缘或表面有拓扑保护的导电态。量子反常霍尔效应可以通过引入自旋轨道耦合相互作用和交换场来实现。文章重点研究了α-T_(3)晶格在两种Rashba自旋轨道耦合相互作用以及交换场的作用下,通过分析体系的相图、能带结构、边缘态和拓扑不变量,理论预测该体系为实现丰富的拓扑相提供了一个平台,包括半金属相和量子反常霍尔相。同时,该体系也是一个实现谷极化量子反常霍尔相的平台。在谷极化量子反常霍尔相中,边缘输运通道集中在单个能谷中,并且在边界上单向传播,可实现无耗散的100%的谷极化。我们的研究不仅发现了丰富的拓扑相,而且为拓扑电子学以及谷电子学应用提供了一个可行的平台。

拓扑绝缘体简介

拓扑绝缘体是最近几年发现的一种全新的物质形态,由于其独特的能带结构,具有零质量的狄拉克费米子及其相关的奇妙物理特性,近些年来引起了人们的广泛关注.同时,它还展现出在自旋电子学和量子计算等领域巨大的应用前景.

自旋陈数理论和时间反演对称破缺的量子自旋霍尔效应

一般认为,量子自旋霍尔效应只有受到时间反演对称性的保护才是稳定的。但是,因为在实际材料中破坏时间反演对称性的微扰往往无法避免,这种受时间反演对称性保护的量子自旋霍尔效应在真实环境中并不稳定。本综述将介绍近期在寻找无需时间反演对称性保护的量子自旋霍尔效应方向上的系列研究进展。我们将证明量子自旋霍尔体系的非平庸拓扑性质在时间反演对称性被破坏后仍然可以完好存在,并通过一个规范讨论,将边缘态一般性质和体能带的非平庸拓扑性质联系起来。进一步,将探讨通过人工消除边缘态时间反演对称性而实现稳定的量子自旋霍尔效应的方案。此外,我们还将介绍自旋陈数理论,自旋陈数是在没有时间反演对称性存在时,表征量子自旋霍尔体系所处不同拓扑相的有效工具。

霍尔效应理论发展过程的研究

以霍尔效应的发展过程为线索,从不同种载流子的经典霍尔效应的出发,系统阐述了霍尔效应的原理、反常霍尔效应、整数量子霍尔效应、分数量子霍尔效应以及自旋霍尔效应理论的发展过程,同时介绍了我国在这方面研究的最新进展.