HgMnTe磁性二维电子气自旋-轨道和交换相互作用研究

通过分析不同温度下HgMnTe磁性二维电子气Shubnikov-de Hass（SdH）振荡的拍频现象，研究了量子阱中电子自旋 轨道相互作用和spd交换相互作用.结果表明：（1）在零磁场下，电子的自旋 轨道相互作用导致电子发生零场自旋分裂；（2）在弱磁场下，电子的自旋-轨道相互作用占主导地位，并受Landau分裂和Zeeman分裂的影响，电子的自旋分裂随磁场增加而减小；（3）在高磁场下，电子的spd交换相互作用达到饱和，电子的自旋分裂主要表现为Zeeman分裂.实验证明了当电子的Zeeman分裂能量与零场 关键词： 磁性二维电子气 Zeeman分裂 Rashba自旋分裂     

Conductance oscillations of a spin-orbit stripe with polarized contacts

We investigate the linear conductance of a stripe of spin-orbit interaction in a 2D electron gas; that is, a 2D region of length l\ell along the transport direction and infinite in the transverse one in which a spin-orbit interaction of Rashba type is present. Polarization in the contacts is described by means of Zeeman fields. Our model predicts two types of conductance oscillations: Ramsauer oscillations in the minority spin transmission, when both spins can propagate, and Fano oscillations when only one spin propagates. The latter are due to the spin-orbit coupling with quasibound states of the non propagating spin. In the case of polarized contacts in antiparallel configuration Fano-like oscillations of the conductance are still made possible by the spin orbit coupling, even though no spin component is bound by the contacts. To describe these behaviors we propose a simplified model based on an ansatz wave function. In general, we find that the contribution for vanishing transverse momentum dominates and defines the conductance oscillations. Regarding the oscillations with Rashba coupling intensity, our model confirms the spin transistor behavior, but only for high degrees of polarization. Including a position dependent effective mass yields additional oscillations due to the mass jumps at the interfaces.     

Weak antilocalization in HgTe quantum wells near a topological transition

The anomalous alternating magnetoresistivity in HgTe quantum wells with thicknesses of 5.8 and 8.3 nm, i.e., near the transition from the direct band spectrum to an inverted spectrum, has been revealed and analyzed. It has been shown that the revealed anomalous alternating magnetoresistivity in wells with an inverted spectrum is well described by the theory developed by S.V. Iordanskii et al. [JETP Lett. 60, 206 (1994)] and W. Knap et al. [Phys. Rev. B 53, 3912 (1996)]. A detailed comparison of the experimental data with the theory indicates the presence of only the cubic term in the spin splitting of the electronic spectrum. The applicability conditions of the mentioned theory are not satisfied in a well with a direct gap and, for this reason, such a certain conclusion is impossible. The results indicate the existence of a strong spin-orbit interaction in symmetric HgTe quantum wells near the topological transition.     

Lateral-surface superlattices in systems with spin-orbit coupling: Quantum states and bloch oscillations in an electric field

The quantum states of a two-dimensional electron gas with spin-orbit coupling located in the periodic potential of a lateral-surface superlattice are studied. The spin-split energy bands and the distribution of spin projections in the Brillouin zone are constructed. Bloch oscillations accompanied by spin precession in superlattices with spin-orbit coupling located in a constant electric field are studied.     

Spin effects in the magneto-oscillations of the capacitance of a two-dimensional gas of semiconductors with Kane and Dirac spectra

The results of experimental investigations and computer modeling of the magneto-oscillations of the capacitance of surface layers with a two-dimensional gas in the narrow-gap semiconductor HgCdTe with direct and inverted band structure are compared. The structure of the Landau levels is calculated by a model that has a clear physical interpretation and is based on the reduction of matrix equations to Schrödinger-like equations with an effective potential in which the terms responsible for nonparabolic and spinor-type effects are easily separable. An analytic approach is developed for describing magneto-oscillation phenomena in the two-dimensional gas of materials with a quasirelativistic spectrum, and the emergence is noted of new theoretical parameters (compared to the parameters of materials with parabolic bands). Finally, the parameters of level broadening in spin-orbit split subsubbands are determined and the dominant scattering mechanisms are discussed.     

Spin edge states in two-dimensional electron systems

We consider the spin edge states, induced by the combined effect of spin-orbit interaction and hard-wall confining potential, in a two-dimensional electron system exposed to a perpendicular quantizing magnetic field. We derive an exact analytical formula for the dispersion relations of spin edge states and analyze their energy spectrum, velocity, and average transverse position. It is shown that by removing the spin degeneracy, spin-orbit interaction splits the spin edge states not only in the energy but also induces their spatial separation. It is revealed that at low magnetic fields, due to the Stark splitting of the spin-resolved edge states, the high-energy bands exhibit anti-crossings. This results in an additional structure in the behavior of the velocity of current-carrying edge states.     

Quarkonium and hydrogen spectra with spin-dependent relativistic wave equation

The non-linear non-perturbative relativistic atomic theory introduces spin in the dynamics of particle motion. The resulting energy levels of hydrogen atom are exactly the same as that of Dirac theory. The theory accounts for the energy due to spin-orbit interaction and for the additional potential energy due to spin and spin-orbit coupling. Spin angular momentum operator is integrated into the equation of motion. This requires modification to classical Laplacian operator. Consequently, the Dirac matrices and the k operator of Dirac’s theory are dispensed with. The theory points out that the curvature of the orbit draws on certain amount of kinetic and potential energies affecting the momentum of electron and the spin-orbit interaction energy constitutes a part of this energy. The theory is developed for spin-1/2 bound state single electron in Coulomb potential and then extended further to quarkonium physics by introducing the linear confining potential. The unique feature of this quarkonium model is that the radial distance can be exactly determined and does not have a statistical interpretation. The established radial distance is then used to determine the wave function. The observed energy levels are used as the input parameters and the radial distance and the string tension are predicted. This ensures 100% conformance to all observed energy levels for the heavy quarkonium.     

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.     

Experimental demonstration of spin geometric phase: radius dependence of time-reversal Aharonov-Casher oscillations

A geometric phase of electron spin is studied in arrays of InAlAs/InGaAs two-dimensional electron gas rings. By increasing the radius of the rings, the time-reversal symmetric Aharonov-Casher oscillations of the electrical resistance are shifted towards weaker spin-orbit interaction regions with their shortened period. We conclude that the shift is due to a modulation of the spin geometric phase, the maximum modulation of which is approximately 1.5 rad. We further show that the Aharonov-Casher oscillations in various radius arrays collapse onto a universal curve if the radius and the strength of Rashba spin-orbit interaction are taken into account. The result is interpreted as the observation of the effective spin-dependent flux through a ring.     

Spin-orbit lateral superlattices: Energy bands and spin polarization in 2DEG

The Bloch spinors, energy spectrum, and spin density in energy bands are studied for a two-dimensional electron gas (2DEG) with Rashba spin-orbit (SO) interaction subject to the one-dimensional (1D) periodic electrostatic potential of a lateral superlattice. The space symmetry of the Bloch spinors with spin parity is studied. It is shown that the Bloch spinors at fixed quasi-momentum describe the standing spin waves with the wavelength equal to the superlattice period. The spin projections in these states have components both parallel and transverse to the 2DEG plane. The anticrossing of the energy dispersion curves due to the interplay between the SO and periodic terms is observed, thus, leading to the spin flip. The relation between the spin parity and the interband optical selection rules is discussed, and the effect of magnetization of the SO superlattice in the presence of an external electric field is predicted. The text was submitted by the authors in English.     

HgTe/HgCdTe量子阱中巨大电子Rashba自旋分裂

主要研究具有倒置能带结构的n-HgTe/HgCdTe第三类量子阱Shubnikov-de Haas（SdH）振荡中的拍频现象.发现在量子阱中电子存在强烈的Rashba自旋分裂，通过对SdH振荡进行三种不同方法的分析：SdH振荡对1/B关系的快速傅里叶变换、SdH振荡中拍频节点分析和对SdH振荡拍频数值拟合，得到了完全一致的电子Rashba自旋分裂能量（28—36 meV）. 关键词： n-HgTe/HgCdTe Shubnikov-de Haas振荡 Rashba自旋分裂     

The Dzyaloshinskii-Moriya interaction in metals

The Dzyaloshinskii-Moriya (DM) interaction in metals is an important mechanism for many magnetic properties. We start with the s-d exchange model and spin-orbit interaction for weak itinerant ferromagnetic systems to establish the form of DM interaction for metallic magnetic systems. The s-d exchange interaction is treated accurately and the conduction electron-mediated magnetism gives a form of DM interaction which is different from that in insulators. The implications of our result to spiral spin states and skyrmion lattices are also discussed.     

Effects of the Rashba spin-orbit coupling on Hofstadter's butterfly

We study the effect of Rashba spin-orbit coupling on the Hofstadter spectrum of a two-dimensional tight-binding electron system in a perpendicular magnetic field. We obtain the generalized coupled Harper spin-dependent equations which include the Rashba spin-orbit interaction and solve for the energy spectrum and spin polarization. We investigate the effect of spin-orbit coupling on the fractal energy spectrum and the spin polarization for some characteristic states as a function of the magnetic flux α and the spin-orbit coupling parameter. We characterize the complexity of the fractal geometry of the spin-dependent Hofstadter butterfly with the correlation dimension and show that it grows quadratically with the amplitude of the spin-orbit coupling. We study some ground state properties and the spin polarization shows a fractal-like behavior as a function of α, which is demonstrated with the exponent close to unity of the decaying power spectrum of the spin polarization. Some degree of spin localization or distribution around +1 or -1, for small spin-orbit coupling, is found with the determination of the entropy function as a function of the spin-orbit coupling. The excited states show a more extended (uniform) distribution of spin states.     

Spin-plasmon oscillations of the two-dimensional electron gas

Interaction of the spins of 2D electrons with an alternating electric field in the plane of the system is considered. It is assumed that the double spin degeneracy is eliminated by the spin-orbit splitting. It is shown that transitions between different spin states produce a narrow absorption band in the degenerate electron gas. In the frequency domain corresponding to these transitions, those frequencies are combined with two-dimensional plasmons; as a result, the plasmon spectrum is modified, and a new type of oscillations occurs, namely, a spin-plasmon polariton. The dispersion law of these oscillations is derived. The problem of the excitation of spin-plasmon polaritons by an external electromagnetic field is solved.     

蓝宝石晶体的光谱精细结构、零场分裂参量及晶体结构

运用不可约张量算法和群理论构造了C3v对称晶场中3d5组念离子的252阶可完全对角化的微扰哈密顿矩阵.用此矩阵计算了Al2O3:Fe3 晶体的光谱精细结构、零场分裂参量(D,a-F)、品体结构,其理论计算值与实验值相符合,并研究了自旋四重态、自旋二重态分别对基态能级的影响,证明了自旋四重态对基态能级的贡献是主要的,自旋二重态对基态能级的贡献虽很小,但却是不可忽略的.进一步研究了SO梢合作用、SS耦合作用对Al2O3:Fe3-品体的光谱精细结构和零场分裂参量的影响,结果发现SO耦合作用是最主要的,SS耦合作用也是不可忽略的.     

Rashba自旋轨道耦合下square-octagon晶格的拓扑相变

本文研究了各向同性square-octagon晶格在内禀自旋轨道耦合、Rashba自旋轨道耦合和交换场作用下的拓扑相变,同时引入陈数和自旋陈数对系统进行拓扑分类.系统在自旋轨道耦合和交换场的影响下会出现许多拓扑非平庸态,包括时间反演对称破缺的量子自旋霍尔态和量子反常霍尔态.特别的是,在时间反演对称破缺的量子自旋霍尔效应中,无能隙螺旋边缘态依然能够完好存在.调节交换场或者填充因子的大小会导致系统发生从时间反演对称破缺的量子自旋霍尔态到自旋过滤的量子反常霍尔态的拓扑相变.边缘态能谱和自旋谱的性质与陈数和自旋陈数的拓扑刻画完全一致.这些研究成果为自旋量子操控提供了一个有趣的途径.     

LiNbO3∶Fe3+晶体的光谱精细结构、零场分裂参量及Jahn-Teller效应

应用不可约张量方法和群的理论构造了三角对称晶场中3d⁵组态离子的252阶可完全对角化的微扰哈密顿矩阵，利用该矩阵计算了LiNbO₃∶Fe³⁺晶体的光谱精细结构、零场分裂、晶体结构、Jahn-Teller(J-T)效应，其理论计算值与实验值相符合，并研究了自旋四重态、自旋二重态分别对基态能级的影响，证明了自旋四重态对基态能级的贡献是主要的，自旋二重态对基态能级的贡献虽很小，但却是不可忽略的.在此基础上,进一步研究了自旋-轨道耦合作用、自旋-自旋耦合作用对LiNbO₃∶Fe³⁺晶体的光谱精细结构和零场分裂参量的影响，发现自旋-轨道耦合作用是最主要的，自旋-自旋耦合作用也是不可忽略的. 研究表明，该种物质的四重态光谱结构中含有J-T效应. 其产生原因是自旋-轨道耦合及三角畸变的共同作用的结果，两者缺一不可.     

Spectroscopy of spin-orbit quantum bits in indium antimonide nanowires

A double quantum dot in the few-electron regime is achieved using local gating in an InSb nanowire. The spectrum of two-electron eigenstates is investigated using electric dipole spin resonance. Singlet-triplet level repulsion caused by spin-orbit interaction is observed. The size and the anisotropy of singlet-triplet repulsion are used to determine the magnitude and the orientation of the spin-orbit effective field in an InSb nanowire double dot. The obtained results are confirmed using spin blockade leakage current anisotropy and transport spectroscopy of individual quantum dots.     

Spin states of holes in Ge/Si nanowire quantum dots

We investigate tunable hole quantum dots defined by surface gating Ge/Si core-shell nanowire heterostructures. In single level Coulomb-blockade transport measurements at low temperatures spin doublets are found, which become sequentially filled by holes. Magnetotransport measurements allow us to extract a g factor g approximately 2 close to the value of a free spin-1/2 particle in the case of the smallest dot. In less confined quantum dots smaller g factor values are observed. This indicates a lifting of the expected strong spin-orbit interaction effects in the valence band for holes confined in small enough quantum dots. By comparing the excitation spectrum with the addition spectrum we tentatively identify a hole exchange interaction strength chi approximately 130 microeV.     

磁性金属材料中交换耦合作用和自旋波的研究

基于交换耦合理论通常使用的近似分析的一般原理, 严格的分析了没有特定假设情况下的磁序范围或有关磁化密度的形式, 及在任何近似下提出一种关于耦合参数的计算方法. 并结合铁磁系统(磁性金属材料Gd, Fe, Ni), 定量的讨论了这种关系的适用范围, 也对自旋波和交换耦合进行了相关分析. 分析表明: 对于近邻磁性原子之间的交换耦合的计算以及在有限波矢量情况下对自旋波谱的计算都得到较为有意义的改进. 提出的交换耦合近似及自旋波谱的关系, 应用于铁磁系统时对近邻原子之间相互作用能给出较好的描述, 或对任何磁体中非完全局域磁化的自旋波谱较大波矢部分给出较合理的描述. 从磁性理论来看, 按照本文模型应用于磁学系统计算得到的结果与实验结果较好的符合.