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.     

Nondissipative spin Hall effect via quantized edge transport

The spin Hall effect in a two-dimensional electron system on honeycomb lattice with both intrinsic and Rashba spin-orbit couplings is studied numerically. Integer quantized spin Hall conductance is obtained at the zero Rashba coupling limit when electron Fermi energy lies in the energy gap created by the intrinsic spin-orbit coupling, in agreement with recent theoretical prediction. While nonzero Rashba coupling destroys electron spin conservation, the spin Hall conductance is found to remain near the quantized value, being insensitive to disorder scattering, until the energy gap collapses with increasing the Rashba coupling. We further show that the charge transport through counterpropagating spin-polarized edge channels is well quantized, which is associated with a topological invariant of the system.     

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。     

Spin and spin-valley Hall effects in a honeycomb lattice with antiferromagnetism and spin-orbit couplings

We study linear response to a longitudinal electric field on an antiferromagnetic honeycomb lattice with intrinsic and Rashba spin-orbit couplings (SOCs). It is found that the spin-valley Hall effect could emerge alone or coexist with the spin Hall effect. The spin and spin-valley Hall conductivities exhibit some peculiarities that depend on the distinct topological states of the graphene lattice. Furthermore, the spin and spin-valley Hall conductivities could be remarkably modulated by changing the Fermi level. Our findings suggest that the antiferromagnetic honeycomb lattice with SOCs is an excellent platform for potential applications of spintronics and valleytronics.     

Resonant intrinsic spin hall effect in p-type GaAs quantum well structure

We study intrinsic spin Hall effect in p-type GaAs quantum well structure described by Luttinger Hamiltonian and a Rashba spin-orbit coupling arising from the structural inversion symmetry breaking. The Rashba term induces an energy level crossing in the lowest heavy hole subband, which gives rise to a resonant spin Hall conductance. The resonance may be used to identify the intrinsic spin Hall effect in experiments.     

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.     

Spin cloud induced around an elastic scatterer by the intrinsic spin hall effect

Similar to the Landauer electric dipole created around an impurity by the electric current, a spin polarized cloud of electrons can be induced by the intrinsic spin Hall effect near a spin independent elastic scatterer. It is shown that in the ballistic range around the impurity, such a cloud appears in the case of Rashba spin-orbit interaction, even though the bulk spin Hall current is absent.     

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.     

Spin Hall effect on edge magnetization and electric conductance of a 2D semiconductor strip

The intrinsic spin Hall effect on spin accumulation and electric conductance in a diffusive regime of a 2D electron gas has been studied for a 2D strip of a finite width. It is shown that the spin polarization near the flanks of the strip, as well as the electric current in the longitudinal direction, exhibit damped oscillations as a function of the width and strength of the Dresselhaus spin-orbit interaction. Cubic terms of this interaction are crucial for spin accumulation near the edges. As expected, no effect on the spin accumulation and electric conductance have been found in case of Rashba spin-orbit interaction.     

Anisotropic intrinsic spin Hall effect in quantum wires

We use numerical simulations to investigate the spin Hall effect in quantum wires in the presence of both Rashba and Dresselhaus spin-orbit coupling. We find that the intrinsic spin Hall effect is highly anisotropic with respect to the orientation of the wire, and that the nature of this anisotropy depends strongly on the electron density and the relative strengths of the Rashba and Dresselhaus spin-orbit couplings. In particular, at low densities, when only one subband of the quantum wire is occupied, the spin Hall effect is strongest for electron momentum along the [N110] axis, which is the opposite of what is expected for the purely 2D case. In addition, when more than one subband is occupied, the strength and anisotropy of the spin Hall effect can vary greatly over relatively small changes in electron density, which makes it difficult to predict which wire orientation will maximize the strength of the spin Hall effect. These results help to illuminate the role of quantum confinement in spin-orbit-coupled systems, and can serve as a guide for future experimental work on the use of quantum wires for spin-Hall-based spintronic applications.     

Spin-Hall transport in a two-dimensional electron system with magnetic impurities

The spin Hall transport properties in a two-dimensional electron system with both Rashba spin-orbit coupling (SOC) and magnetic impurities are investigated. Electrons are scattered by impurities through an exchange interaction that leads to spin flip-flop processes and so changes the spin Hall effect induced by the SOC. The spin Hall conductance is calculated in a 4-terminal system using the Landauer-Buttiker formula and Green function approach. In comparison with the simulation results on nonmagnetic impurities doping systems, our results reveal that the spin Hall conductance is still nonzero in a system with a large density of magnetic impurities and a finite intensity of the exchange interaction between the electrons and impurities, and its sign may be altered when the doping density and interaction strength are large enough.     

Charge current driven by spin dynamics in disordered Rashba spin-orbit system

Pumping of charge current by spin dynamics in the presence of the Rashba spin-orbit interaction is theoretically studied. Considering a disordered electron, the exchange coupling and spin-orbit interactions are treated perturbatively. It is found that the dominant current induced by spin dynamics is interpreted as a consequence of the conversion from spin current via the inverse spin Hall effect. We also find that the current has an additional component from a fictitious conservative field. The results are applied to the case of a moving domain wall.     

Interplay of Rashba effect and spin Hall effect in perpendicular Pt/Co/MgO magnetic multilayers

The interplay of the Rashba effect and the spin Hall effect originating from current induced spin–orbit coupling was investigated in the as-deposited and annealed Pt/Co/MgO stacks with perpendicular magnetic anisotropy. The above two effects were analyzed based on Hall measurements under external magnetic fields longitudinal and vertical to dc current,respectively. The coercive field as a function of dc current in vertical mode with only the Rashba effect involved decreases due to thermal annealing. Meanwhile, spin orbit torques calculated from Hall resistance with only the spin Hall effect involved in the longitudinal mode decrease in the annealed sample. The experimental results prove that the bottom Pt/Co interface rather than the Co/MgO top one plays a more critical role in both Rashba effect and spin Hall effect.     

Band structures of carbon nanotube with spin-orbit coupling interaction

We explore the band structures of single-walled carbon nanotubes (SWCNTs) with two types of spin-orbit couplings. The obtained results indicate that weak Rashba spin-orbit coupling interaction can lead to the breaking of four-fold degeneracy in all tubes even though without the intrinsic SO coupling. The asymmetric splitting between conduction bands and valence bands is caused by both SO couplings at the same time. When the ratio of Rashba spin-orbit coupling to the intrinsic spin-orbit coupling is larger than 3, metallic zigzag nanotube is always metallic conductor, on the contrary it becomes semiconducting properties. However, only when this ratio is equal to about 3 or the intrinsic spin-orbit coupling is much weak, the metallic armchair nanotube still holds the metallic behavior in transport.     

Nonequilibrium spin Hall accumulation in ballistic semiconductor nanostructures

We demonstrate that the flow of a longitudinal unpolarized current through a ballistic two-dimensional electron gas with Rashba spin-orbit coupling will induce a nonequilibrium spin accumulation which has opposite signs for the two lateral edges and is, therefore, the principal observable signature of the spin Hall effect in two-probe semiconductor nanostructures. The magnitude of its out-of-plane component is gradually diminished by static disorder, while it can be enhanced by an in-plane transverse magnetic field. Moreover, our prediction of the longitudinal component of the spin Hall accumulation, which is insensitive to the reversal of the bias voltage, offers direct evidence to differentiate experimentally between the extrinsic, intrinsic, and mesoscopic spin Hall mechanisms.     

Rashba spin-orbit effect on dwell time of electrons tunneling through semiconductor barrier

A study on characteristics of electrons tunneling through semiconductor barrier is evaluated, in which we take into account the effects of Rashba spin-orbit interaction. Our numerical results show that Rashba spin-orbit effect originating from the inversion asymmetry can give rise to the spin polarization. The spin polarization does not increase linearly but shows obvious resonant features as the strength of Rashba spin-orbit coupling increases, and the amplitudes of spin polarization can reach the highest around the first resonant energy level. Furthermore, it is found that electrons with different spin orientations will spend quite different time through the same heterostructures. The difference of the dwell time between spin-up and spin-down electrons arise from the Rashba spin-orbit coupling. And it is also found that the dwell time will reach its maximum at the first resonant energy level. It can be concluded that, in the time domain, the tunneling processes of the spin-up and spin-down electrons can be separated by modulating the strength of Rashba spin-orbit coupling. Study results indicate that Rashba spin-orbit effect can cause a nature spin filter mechanism in the time domain.     

Effect of Rashba interaction at normal metal/insulator interface on spin-orbit torque of ferromagnet/normal metal/insulator trilayers

Based on a spin drift-diffusion model, we theoretically investigate the spin-orbit torque in ferromagnet/normal metal/insulator trilayers with considering the Rashba interfacial spin-orbit coupling at the normal metal/insulator interface. We find that the spin-orbit torque shows the opposite normal-metal-thickness dependences for the bulk spin-orbit coupling effect in the normal metal layer and for the interfacial spin-orbit coupling effect at the normal metal/insulator interface, offering a way to disentangle these two spin-orbit coupling effects. Moreover, we show that the conventional interpretation based on the bulk spin-orbit coupling effect overestimates the spin Hall angle and underestimates the spin diffusion length of the normal metal layer, when the interfacial contribution is non-negligible. Our result, a concise analytic expression of the spin-orbit torque considering both bulk and interface spin-orbit coupling effects, will be useful to design and interpret experiments on spin-orbit torque experiments in ferromagnet/normal metal/insulator trilayers.     

Current-induced spin polarization in a spin-polarized two-dimensional electron gas with spin-orbit coupling

The current-induced spin polarization (CISP) is investigated in a combined Rashba-Dresselhaus spin-orbit-coupled two-dimensional electron gas, subjected to a homogeneous out-of-plane magnetization. It is found that, in addition to the usual collision-related in-plane parts of CISP, there are two impurity-density-free contributions, arising from intrinsic and disorder-mediated mechanisms. The intrinsic parts of spin polarization are related to the Berry curvature, analogous with the anomalous and spin Hall effects. For short-range collision, the disorder-mediated spin polarizations completely cancel the intrinsic ones and the total in-plane components of CISP equal those for systems without magnetization. However, for remote disorders, this cancellation does not occur and the total in-plane components of CISP strongly depend on the spin-orbit interaction coefficients and magnetization for both pure Rashba and combined Rashba-Dresselhaus models.     

Electrical manipulation and measurement of spin properties of quantum spin Hall edge states

We study the effects of a gate-controlled Rashba spin-orbit coupling to quantum spin Hall edge states in HgTe quantum wells. A uniform Rashba coupling can be employed in tuning the spin orientation of the edge states while preserving the time-reversal symmetry. We introduce a sample geometry where the Rashba coupling can be used in probing helicity by purely electrical means without requiring spin detection, application of magnetic materials or magnetic fields. In the considered setup a tilt of the spin orientation with respect to the normal of the sample leads to a reduction in the two-terminal conductance with current-voltage characteristics and temperature dependence typical of Luttinger liquid constrictions.