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 C_s 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, C_s 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.     

Two-dimensional topological insulator state and topological phase transition in bilayer graphene

We show that gated bilayer graphene hosts a strong topological insulator (TI) phase in the presence of Rashba spin-orbit (SO) coupling. We find that gated bilayer graphene under preserved time-reversal symmetry is a quantum valley Hall insulator for small Rashba SO coupling λ(R), and transitions to a strong TI when λ(R)>√[U(2)+t(⊥)(2)], where U and t(⊥) are, respectively, the interlayer potential and tunneling energy. Different from a conventional quantum spin Hall state, the edge modes of our strong TI phase exhibit both spin and valley filtering, and thus share the properties of both quantum spin Hall and quantum valley Hall insulators. The strong TI phase remains robust in the presence of weak graphene intrinsic SO coupling.     

Tunable valley filter efficiency by spin–orbit coupling in silicene nanoconstrictions

Valley filter is a promising device for producing valley polarized current in graphene-like two-dimensional honeycomb lattice materials. The relatively large spin–orbit coupling in silicene contributes to remarkable quantum spin Hall effect, which leads to distinctive valley-dependent transport properties compared with intrinsic graphene. In this paper,quantized conductance and valley polarization in silicene nanoconstrictions are theoretically investigated in quantum spinHall insulator phase. Nearly perfect valley filter effect is found by aligning the gate voltage in the central constriction region. However, the valley polarization plateaus are shifted with the increase of spin–orbit coupling strength, accompanied by smooth variation of polarization reversal. Our findings provide new strategies to control the valley polarization in valleytronic devices.     

Topological phases of silicene and germanene in an external magnetic field: Quantitative results

We investigate the topological phases of silicene and germanene that arise due to the strong spin–orbit interaction in an external perpendicular magnetic field. Below and above a critical field of 10 T, respectively, we demonstrate for silicene under 3% tensile strain quantum spin Hall and quantum anomalous Hall phases. Not far above the critical field, and therefore in the experimentally accessible regime, we obtain an energy gap in the meV range, which shows that the quantum anomalous Hall phase can be realized experimentally in silicene, in contrast to graphene (tiny energy gap) and germanene (enormous field required). (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Silicene on substrates:A theoretical perspective

Silicene, as the silicon analog of graphene, is successfully fabricated by epitaxially growing it on various substrates.Like free-standing graphene, free-standing silicene possesses a honeycomb structure and Dirac-cone-shaped energy band,resulting in many fascinating properties such as high carrier mobility, quantum spin Hall effect, quantum anomalous Hall effect, and quantum valley Hall effect. The existence of the honeycomb crystal structure and the Dirac cone of silicene is crucial for observation of its intrinsic properties. In this review, we systematically discuss the substrate effects on the atomic structure and electronic properties of silicene from a theoretical point of view, especially with emphasis on the changes of the Dirac cone.     

Intrinsic spin Hall effect in silicene: transition from spin Hall to normal insulator

An intrinsic contribution to the spin Hall effect in two‐dimensional silicene is considered theoretically within the linear response theory and Green's function formalism. When an external voltage normal to the silicene plane is applied, the spin Hall conductivity is shown to reveal a transition from the spin Hall insulator phase at low bias to the conventional insulator phase at higher voltages. This transition resembles the recently reported phase transition in bilayer graphene. The spin–orbit interaction responsible for this transition in silicene is much stronger than in graphene, which should make the transition observable experimentally. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Spin and valley dependent line-type resonant peaks in electrically and magnetically modulated silicene quantum structures

A barrier with a tunable spin-valley dependent energy gap in silicene could be used as a spin and valley filter. Meanwhile, special resonant modes in unique quantum structure can act as energy filters. Hence we investigate valley and spin transport properties in the potential silicene quantum structures, i.e., single ferromagnetic barrier, single electromagnetic barrier and double electric barriers. Our quantum transport calculation indicates that quantum devices of high accuracy and efficiency (100% polarization), based on modulated silicene quantum structures, can be designed for valley, spin and energy filtering. These intriguing features are revealed by the spin, valley dependent line-type resonant peaks. In addition, line-type peaks in different structure depend on spin and valley diversely. The filter we proposed is controllable by electric gating.     

电子的谷自由度

电子在晶格周期性势场影响下的运动遵循布洛赫定理. 布洛赫电子除了具有电荷和自旋两个内禀自由度外, 还有其他内禀自由度. 能带色散曲线上的某些极值点作为谷自由度, 具有独特的电子结构和运动规律. 本文从布洛赫电子的谷自由度出发, 简单介绍传统半导体的谷电子性质研究现状, 并重点介绍新型二维材料体系, 如石墨烯、硅烯、硫族化合物等材料中谷相关的物理特性. 有效利用谷自由度的新奇输运特性, 将其作为信息的载体可以制作出新颖的纳米光电子器件, 并有望造就下一代纳电子器件的新领域, 即谷电子学(valleytronics).     

半导体中自旋轨道耦合及自旋霍尔效应

本文主要评述和介绍半导体微结构中自旋轨道耦合的研究和最近的研究进展。我们细致地讨论了半导体微结构中自旋轨道耦合的物理起源和窄带隙半导体量子阱中的自旋霍尔效应。我们发现目前国际上广泛采用的线性Rashba模型在较大的电子平面波矢处失效:即自旋轨道耦合导致的能带自旋劈裂不再随电子波矢的增加而增加,而是开始下降,即出现强烈的非线性行为。这种非线性的行为起源于导带和价带间耦合的减弱。这种非线性行为还会导致电子的D’yakonov-Perel’自旋弛豫速率在较高能量处下降,与线性模型的结果完全相反。在此基础上,我们构造统一描述电子和空穴自旋霍尔效应的理论框架。我们的方法可以非微扰地计入自旋轨道耦合对本征自旋霍尔效应的影响。我们将此方法应用于强自旋轨道耦合的情形,即窄带隙CdHgTe/CdTe半导体量子阱。我们发现调节外电场或量子阱的阱宽可以作为导致量子相变和本征自旋霍尔效应的开关。我们的工作可能会为区别和实验验证本征自旋霍尔效应提供物理基础。     

Thermoelectric properties of magnetic configurations of graphene-like nanoribbons in the presence of Rashba and spin–orbit interactions

In this paper we investigate the influence of spin–orbit interaction and two types of Rashba interaction (intrinsic and extrinsic) on magnetic and thermoelectric properties of graphene-like zigzag nanoribbons based on the honeycomb lattice. We utilize the Kane-Mele model with additional Rashba interaction terms. Magnetic structure is described by the electron-electron Coulomb repulsion reduced to the on-site interaction (Hubbard term) in the mean field approximation. We consider four types of magnetic configurations: ferromagnetic and antiferromagnetic with in-plane and out-of plane direction of magnetization. Firstly, we analyze the influence of extrinsic Rashba coupling on systems with negligible spin–orbit interaction, e.g. graphene of an appropriate substrate. Secondly, we discuss the interplay between spin–orbit and intrinsic Rashba interactions. This part is relevant to materials with significant spin–orbit coupling such as silicene and stanene.