Intrinsic contribution to spin Hall and spin Nernst effects in a bilayer graphene

We consider intrinsic contributions to the spin Hall and spin Nernst effects in a bilayer graphene. The relevant electronic spectrum is obtained from the tight binding Hamiltonian, which also includes the intrinsic spin-orbit interaction. The corresponding spin Hall and spin Nernst conductivities are compared with those obtained from effective low-energy k ?p and reduced Hamiltonians, which are appropriate for states in the vicinity of the Fermi level of a neutral bilayer graphene. Both conductivities are determined within the linear response theory and Green function formalism. The influence of an external voltage between the two atomic sheets is also considered. The results reveal a transition from the topological spin Hall insulator phase at low voltages to conventional insulator phase at larger voltages.     

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.     

Assessment of bilayer silicene to probe as quantum spin and valley Hall effect

Silicene takes precedence over graphene due to its buckling type structure and strong spin orbit coupling. Motivated by these properties, we study the silicene bilayer in the presence of applied perpendicular electric field and intrinsic spin orbit coupling to probe as quantum spin/valley Hall effect. Using analytical approach, we calculate the spin Chern-number of bilayer silicene and then compare it with monolayer silicene. We reveal that bilayer silicene hosts double spin Chern-number as compared to single layer silicene and therefore accordingly has twice as many edge states in contrast to single layer silicene. In addition, we investigate the combined effect of intrinsic spin orbit coupling and the external electric field, we find that bilayer silicene, likewise single layer silicene, goes through a phase transitions from a quantum spin Hall state to a quantum valley Hall state when the strength of the applied electric field exceeds the intrinsic spin orbit coupling strength. We believe that the results and outcomes obtained for bilayer silicene are experimentally more accessible as compared to bilayer graphene, because of strong SO coupling in bilayer silicene.     

Time-reversal-symmetry-broken quantum spin Hall effect

The quantum spin Hall (QSH) state of matter is usually considered to be protected by time-reversal (TR) symmetry. We investigate the fate of the QSH effect in the presence of the Rashba spin-orbit coupling and an exchange field, which break both inversion and TR symmetries. It is found that the QSH state characterized by nonzero spin Chern numbers C(±) = ±1 persists when the TR symmetry is broken. A topological phase transition from the TR-symmetry-broken QSH phase to a quantum anomalous Hall phase occurs at a critical exchange field, where the bulk band gap just closes. It is also shown that the transition from the TR-symmetry-broken QSH phase to an ordinary insulator state cannot happen without closing the band gap.     

Z2 topological order and the quantum spin Hall effect

The quantum spin Hall (QSH) phase is a time reversal invariant electronic state with a bulk electronic band gap that supports the transport of charge and spin in gapless edge states. We show that this phase is associated with a novel Z2 topological invariant, which distinguishes it from an ordinary insulator. The Z2 classification, which is defined for time reversal invariant Hamiltonians, is analogous to the Chern number classification of the quantum Hall effect. We establish the Z2 order of the QSH phase in the two band model of graphene and propose a generalization of the formalism applicable to multiband and interacting systems.     

Quantum spin Hall effect in graphene

We study the effects of spin orbit interactions on the low energy electronic structure of a single plane of graphene. We find that in an experimentally accessible low temperature regime the symmetry allowed spin orbit potential converts graphene from an ideal two-dimensional semimetallic state to a quantum spin Hall insulator. This novel electronic state of matter is gapped in the bulk and supports the transport of spin and charge in gapless edge states that propagate at the sample boundaries. The edge states are nonchiral, but they are insensitive to disorder because their directionality is correlated with spin. The spin and charge conductances in these edge states are calculated and the effects of temperature, chemical potential, Rashba coupling, disorder, and symmetry breaking fields are discussed.     

Topological spin Hall states, charged skyrmions, and superconductivity in two dimensions

We study the properties of two dimensional topological spin Hall insulators which arise through spontaneous breakdown of spin symmetry in systems that are spin rotation invariant. Such a phase breaks spin rotation but not time reversal symmetry and has a vector order parameter. Skyrmion configurations in this vector order parameter are shown to have an electric charge that is twice the electron charge. When the spin Hall order is destroyed by condensation of Skyrmions superconductivity results. This may happen either through doping or at fixed filling by tuning interactions to close the Skyrmion gap. In the latter case the superconductor-spin Hall insulator quantum phase transition can be second order even though the two phases break distinct symmetries.     

Quantum spin Hall effect in silicene and two-dimensional germanium

We investigate the spin-orbit opened energy gap and the band topology in recently synthesized silicene as well as two-dimensional low-buckled honeycomb structures of germanium using first-principles calculations. We demonstrate that silicene with topologically nontrivial electronic structures can realize the quantum spin Hall effect (QSHE) by exploiting adiabatic continuity and the direct calculation of the Z(2) topological invariant. We predict that the QSHE can be observed in an experimentally accessible low temperature regime in silicene with the spin-orbit band gap of 1.55 meV, much higher than that of graphene. Furthermore, we find that the gap will increase to 2.9 meV under certain pressure strain. Finally, we also study germanium with a similar low-buckled stable structure, and predict that spin-orbit coupling opens a band gap of 23.9 meV, much higher than the liquid nitrogen temperature.     

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)     

Effects of interaction on quantum spin Hall insulators

We study the S(z)-conserving quantum spin Hall insulator in the presence of Hubbard U from a field theory point of view. The main findings are the following. (1) For arbitrarily small U the edges possess power-law correlated antiferromagnetic XY local moments. Gapless charge excitations arise from the Goldstone-Wilczek mechanism. (2) Electron tunneling between opposite edges allows vortex instantons to proliferate when K, the XY stiffness constant, satisfies 4πK+(4πK)(-1)<4. When the preceding inequality is violated, the edge modes remain gapless despite the sample width being finite. (3) The phase transition from the topological insulator to the large U antiferromagnetic insulator is triggered by the condensation of magnetic excitons. (4) In the large U antiferromagnetic insulating phase the magnetic vortices carry charges proportional to the square magnitude of the antiferromagnetic order parameter.     

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.     

光自旋霍尔效应中的交叉偏振特性研究

从光束角谱理论出发建立了描述光自旋霍尔效应的傍轴传输模型, 利用这一模型分析了光自旋霍尔效应中的交叉偏振特性. 通过分析交叉偏振效应强度和入射角变化的规律, 发现交叉偏振效应越强, 光自旋霍尔效应中的自旋分裂越大. 为便于实验观察, 将入射角选在光自旋霍尔效应较强的布儒斯特角附近, 观测到了强的交叉偏振效应. 增大交叉偏振分量的同时减小初始偏振分量, 可显著增强光自旋霍尔效应. 这一调控方法为研制基于光自旋霍尔效应的新型光子器件提供了理论基础.     

基于Pancharatnam-Berry相位和动力学相位调控纵向光子自旋霍尔效应

提出了一种基于Pancharatnam-Berry相位和动力学相位操控纵向光子自旋霍尔效应的方法.理论分析表明:当光场通过一个由Pancharatnam-Berry相位透镜和动力学相位透镜构成的透镜组时,透镜组会存在两个自旋相关的焦点.首先,当左旋和右旋圆偏振光通过微结构相位延迟为π的Pancharatnam-Berry相位透镜时,由于Pancharatnam-Berry相位的自旋相关性,两个圆偏振分量会获得符号相反的Pancharatnam-Berry相位而导致其中一个被聚焦而另一个发散.然后,在Pancharatnam-Berry相位透镜后再插入普通透镜引入动力学相位调制,由于动力学相位是自旋无关,使得这一透镜组,可以在合适的条件下使不同自旋态的光子分别聚焦于纵向上不同焦点处.纵向自旋分裂由两透镜焦距及间距共同决定,因此可以通过改变两个透镜的焦距及其间距获得任意的纵向自旋分裂值.最后,搭建了一套实验装置,所得实验结果与理论结果一致.     

Photoinduced anisotropic edge states and signatures of nonequilibrium spin polarization in silicene nanoribbons

Most topological phase transitions are accompanied by the emergence of surface/edge states with spin dependence. Usually, the quantized Hall conductivity cannot characterize the anisotropic transports and spin dependence of topological states. Here, we study the intricate topological phase transition and the anisotropic behavior of edge states in silicene nanoribbon submitted to an electric field or/and a light irradiation. It is interesting to find that a circularly polarized light can induce a type-II quantum anomaly Hall phase, which is manifested as the high Chern number and the strong anisotropic edge states. Besides the measurement of the quantized Hall conductivity, we further propose to probe these topological phase transitions and the anisotropy of edge states by measuring the current-induced nonequilibrium spin polarization. It is found that the spin polarization exhibits more signatures about the behavior of surface/edge states, beyond the quantized Hall conductivity, especially for spin-dependent transports with different velocities.     

Enhanced photonic spin Hall effect with subwavelength topological edge states

Photonic structures offer unique opportunities for controlling light‐matter interaction, including the photonic spin Hall effect associated with the transverse spin‐dependent displacement of a light beam that propagates in specially designed optical media. However, due to small spin‐orbit coupling, the photonic spin Hall effect is usually weak at the nanoscale. Here we suggest theoretically and demonstrate experimentally, in both optics and microwave experiments, the photonic spin Hall effect enhanced by topologically protected edge states in subwavelength arrays of resonant dielectric particles. Based on direct near‐field measurements, we observe the selective excitation of the topological edge states controlled by the handedness of the incident light. Additionally, we reveal the main requirements to the symmetry of photonic structures to achieve the topology‐enhanced spin Hall effect, and also analyse the robustness of the photonic edge states against the long‐range coupling.

     

Spin textures of strongly correlated spin Hall quantum dots

We study the spin ordering of a quantum dot defined via magnetic barriers in an interacting quantum spin Hall edge. The spin‐resolved density–density correlation functions are computed. We show that strong electron interactions induce a ground state with a highly correlated spin pattern. The crossover from the liquid‐type correlations at weak interactions to the ground state spin texture found at strong interactions parallels the formation of a one‐dimensional Wigner molecule in an ordinary strongly interacting quantum dot.

     

Quantum phase transition of cold atoms trapped in optical lattices

We review our recent theoretical advances in phase transition of cold atoms in optical lattices, such as triangular lattice, honeycomb lattice, and Kagomé lattice. By employing the new developed numerical methods called dynamical cluster approximation and cellular dynamical mean-field theory, the properties in different phases of cold atoms in optical lattices are studied, such as density of states, Fermi surface and double occupancy. On triangular lattice, a reentrant behavior of phase translation line between Fermi liquid state and pseudogap state is found due to the Kondo effect. We find the system undergoes a second order Mott transition from a metallic state into a Mott insulator state on honeycomb lattice and triangular Kagomé lattice. The stability of quantum spin Hall phase towards interaction on honeycomb lattice with spin-orbital coupling is systematically discussed. And we investigate the transition from quantum spin Hall insulator to normal insulator in Kagomé lattice which includes a nearest-neighbor intrinsic spin-orbit coupling and a trimerized Hamiltonian. In addition, we propose the experimental protocols to observe these phase transition of cold atoms in optical lattices.     

Quantum spin Hall effect in inverted type-II semiconductors

The quantum spin Hall (QSH) state is a topologically nontrivial state of quantum matter which preserves time-reversal symmetry; it has an energy gap in the bulk, but topologically robust gapless states at the edge. Recently, this novel effect has been predicted and observed in HgTe quantum wells and in this Letter we predict a similar effect arising in Type-II semiconductor quantum wells made from InAs/GaSb/AlSb. The quantum well exhibits an "inverted" phase similar to HgTe/CdTe quantum wells, which is a QSH state when the Fermi level lies inside the gap. Due to the asymmetric structure of this quantum well, the effects of inversion symmetry breaking are essential. Remarkably, the topological quantum phase transition between the conventional insulating state and the quantum spin Hall state can be continuously tuned by the gate voltage, enabling quantitative investigation of this novel phase transition.     

异常霍尔效应和自旋霍尔效应

异常霍尔效应和自旋霍尔效应是在常规霍尔效应的基础上引发出的2种新现象.本文介绍了这2种现象及其原理和潜在的应用.