准一维半导体量子点中电偶极自旋共振的物理机理

半导体量子点中的电子自旋具有较长相干时间以及可扩展性的特点, 在近十几年来引起了人们的广泛兴趣. 人们常常利用电子自旋共振技术来对单个自旋进行操纵. 这样不但需要一个静磁场来使电子产生赛曼劈裂, 同时还需要一个与之垂直的局域振荡磁场. 但是, 在实验上产生足够强且具有固定频率的局域磁场是比较困难的. 后来人们发现, 局域的振荡电场也可以操纵单个电子自旋, 也就是所谓的电偶极自旋共振. 众所周知, 自旋只有自旋磁矩, 不会与电场有任何直接的相互作用. 所以, 电偶极自旋共振的发生必须依赖于某些媒质. 这些媒质包括：量子点材料中的自旋轨道耦合作用, 量子点中的局域磁场梯度, 以及量子点中电子自旋与核自旋的超精细相互作用. 这些媒质能诱导出自旋与电场之间间接的相互作用, 从而外电场操纵单个电子自旋得以实现. 本文总结归纳了目前半导体量子点系统中发生电偶极自旋共振的三种主要物理机理.     

The effects of electron–phonon interaction on anisotropic RKKY interaction in graphene nanoribbon

We study the Ruderman–Kittle–Kasuya–Yosida (RKKY) interaction in doped armchair graphene nanoribbon. The effects of both external magnetic field and electron-Holstein phonon on RKKY interaction have been addressed. RKKY interaction as a function of distance between localized moments has been analyzed. It has been shown that a magnetic field along the z-axis mediates an anisotropic interaction which corresponds to a XXZ model interaction between two magnetic moments. In order to calculate the exchange interaction along arbitrary direction between two magnetic moments, we should obtain both transverse and longitudinal static spin susceptibilities of armchair graphene nanoribbon in the presence of electron-phonon coupling and magnetic field. The spin susceptibility components are calculated using the spin dependent Green’s function approach for Holstein model Hamiltonian. The effects of spin polarization on the dependence of exchange interaction on distance between moments are investigated via calculating correlation function of spin density operators. Our results show the influences of magnetic field on the spatial behavior of in-plane and longitudinal RKKY interactions are different in the presence of magnetic field.     

Untersuchung von elektrischer Hyperfeinstruktur-Wechselwirkung in Hafniumammoniumhexafluorid-Einkristallen durch γγ-Winkelkorrelationsmessungen

The angular correlation of the 133 keV-482 keV-yy-cascade in the decay of Hf¹⁸¹ is strongly attenuated if solid sources of hafniumammoniumhexafluoride are used. The unperturbed correlation was observed however when a single crystal of hafniumammoniumhexafluoride was used whose main axis pointed into the direction of one of the two detectors. This proves that the perturbation is static and that the maximum component of the electric field gradient at the position of the hafnium nucleus coincides with the direction of the main axis of the crystal. The anisotropy of the angular correlation was measured as a function of the direction of the crystal axis. The results agree with the theoretical predicted functions for a strong electric quadrupole interaction. Then we combined the intrinsic electric field with an external magnetic field. The magnetic field direction was chosen parallel to thez-axis of the electric field gradient and perpendicular to the plane of the detectors. The theory for axially symmetric field gradients predicts a maximum of the anisotropy of the angular correlation for a magnetic field strength at which resonance exists between electric and magnetic precession. For a strong electric interaction the maxium anisotropy has half the value of the unperturbed correlation. In our case the electric quadrupole interaction was so strong that we could not reach the resonance even when we applied external magnetic fields up to 48000 gauss. The observed anisotropies were too large however to be fitted by theoretical curves which were calculated under the assumption that the field gradient has axial symmetry. Therefore we developed the theory for non-axially symmetric electric field gradients. Now a fit was possible and gave unique solutions for the strength of the electric hyperfine interaction as well as for the asymmetry coefficient of the electric field gradient tensor. The accuray of these results was not very high but the strength of the electric hyperfine interaction was found to be small enough to make a direct observation of the electric spin rotation by the differential angular correlation method possible. The observed pattern confirmed the non-axially symmetry of the electric field gradient and we derived the following parameters:

$$\omega _{E_0 } = \left( {570 \pm 30} \right)MHz\left( {\omega _{E_0 } = electric interaction frequency = \frac{{6eQ \cdot \left| {V_{zz} } \right|}}{{4I \cdot \left( {2I - 1} \right) \cdot \rlap{--} h}}} \right)$$     

Electronic structure of paramagnetic In<Subscript>1-x</Subscript>Mn<Subscript>x</Subscript> As nanowires

The electronic structure, spin splitting energies, and g factors of paramagnetic In_1-xMn_xAs nanowires under magnetic and electric fields are investigated theoretically including the sp-d exchange interaction between the carriers and the magnetic ion. We find that the effective g factor changes dramatically with the magnetic field. The spin splitting due to the sp-d exchange interaction counteracts the Zeeman spin splitting. The effective g factor can be tuned to zero by the external magnetic field. There is also spin splitting under an electric field due to the Rashba spin-orbit coupling which is a relativistic effect. The spin-degenerated bands split at nonzero k_z (k_z is the wave vector in the wire direction), and the spin-splitting bands cross at k_z = 0, whose k_z-positive part and negative part are symmetrical. A proper magnetic field makes the k_z-positive part and negative part of the bands asymmetrical, and the bands cross at nonzero k_z. In the absence of magnetic field, the electron Rashba coefficient increases almost linearly with the electric field, while the hole Rashba coefficient increases at first and then decreases as the electric field increases. The hole Rashba coefficient can be tuned to zero by the electric field.     

Influence of quadrupole–quadrupole-type interaction on the chaotic dynamics of $$\alpha $$-helical proteins

We calculate the electronic band dispersion of graphene monolayer on a two-dimensional transition metal dichalcogenide substrate (GrTMD) around K and \(\mathbf{K}^{\prime }\) points by taking into account the interplay of the ferromagnetic impurities and the substrate-induced interactions. The latter are (strongly enhanced) intrinsic spin–orbit interaction (SOI), the extrinsic Rashba spin–orbit interaction (RSOI) and the one related to the transfer of the electronic charge from graphene to substrate. We introduce exchange field (M) in the Hamiltonian to take into account the deposition of magnetic impurities on the graphene surface. The cavalcade of the perturbations yield particle–hole symmetric band dispersion with an effective Zeeman field due to the interplay of the substrate-induced interactions with RSOI as the prime player. Our graphical analysis with extremely low-lying states strongly suggests the following: The GrTMDs, such as graphene on \(\hbox {WY}_{2}\), exhibit (direct) band-gap narrowing / widening (Moss–Burstein (MB) gap shift) including the increase in spin polarisation (P) at low temperature due to the increase in the exchange field (M) at the Dirac points. The polarisation is found to be electric field tunable as well. Finally, there is anticrossing of non-parabolic bands with opposite spins, the gap closing with same spins, etc. around the Dirac points. A direct electric field control of magnetism at the nanoscale is needed here. The magnetic multiferroics, like \(\hbox {BiFeO}_{3}\) (BFO), are useful for this purpose due to the coupling between the magnetic and electric order parameters.     

Theory of magnetic switching of ferroelectricity in spiral magnets

We propose a microscopic theory for magnetic switching of electric polarization (P) in the spin-spiral multiferroics by taking TbMnO3 and DyMnO3 as examples. We reproduce their phase diagrams under a magnetic field Hex by Monte Carlo simulation of an accurate spin model and reveal that competition among the Dzyaloshinskii-Moriya interaction, spin anisotropy, and spin exchange is controlled by the applied Hex, resulting in magnetic transitions accompanied by reorientation or vanishing of P. We also discuss the relevance of the proposed mechanisms to many other multiferroics such as LiCu2O2, MnWO4, and Ni3V2O4.     

Entanglement in a three spin system controlled by electric and magnetic fields

We study the effect of electric field and magnetic flux on spin entanglement in an artificial triangular molecule built of coherently coupled quantum dots. In a subspace of doublet states an explicit relation of concurrence with spin correlation functions and chirality is presented. The electric field modifies superexchange correlations and shifts many-electron levels (the Stark effect), as well as changing spin correlations. For some specific orientation of the electric field one can observe monogamy, for which one of the spins is separated from two others. Moreover, the Stark effect manifests itself in a different spin entanglement for small and strong electric fields. The role of magnetic flux is opposite: it leads to circulation of spin supercurrents and spin delocalization.     

Probing Dual Asymmetric Transverse Spin Angular Momentum in Tightly Focused Vector Beams in Optical Tweezers

The spin-orbit interaction (SOI) of light generated by tight focusing in optical tweezers is regularly employed in generating angular momentum - both spin and orbital - the effects being extensively observed in trapped mesoscopic particles. Specifically, the transverse spin angular momentum (TSAM), which arises due to the longitudinal component of the electromagnetic field generated by tight focusing is of special interest, both in terms of fundamental studies and associated applications. This study provides an effective and optimal strategy for generating TSAM in optical tweezers by tightly focusing first-order radially and azimuthally polarized vector beams with no intrinsic angular momentum (AM) into a refractive index stratified medium. The choice of such input fields ensures that the longitudinal spin angular momentum (LSAM) arising from the electric (magnetic) field for the radial (azimuthal) polarization is zero. As a result, the effects of the electric and magnetic TSAM are exclusively observed separately in the case of input first-order radially and azimuthally polarized vector beams on single optically trapped birefringent particles. This research opens up new and simple avenues for exotic and complex particle manipulation in optical tweezers.     

Magnetoelectric memory effect in the Y-type hexaferrite BaSrZnMgFe_(12)O_(22)

We report on the magnetic and magnetoelectric properties of the Y-type hexaferrite BaSrZnMgFe_(12)O_(22),which undergoes transitions from a collinear ferrimagnetic phase to a proper screw phase at 310 K and to a longitudinal conical phase at 45 K.Magnetic and electric measurements revealed that the magnetic structure with spiral spin order can be modified by applying a magnetic field,resulting in magnetically controllable electric polarization.It was observed that BaSrZnMgFe_(12)O_(22)exhibits an anomalous magnetoelectric memory effect:the ferroelectric state can be partially recovered from the paraelectric phase with collinear spin structure by reducing magnetic field at 20 K.We ascribe this memory effect to the pinning of multiferroic domain walls,where spin chirality and structure are preserved even in the nonpolar collinear spin state.     

金属表面Rashba自旋轨道耦合作用研究进展

自旋轨道耦合是电子自旋与轨道相互作用的桥梁, 它提供了利用外电场来调控电子的轨道运动、进而调控电子自旋状态的可能. 固体材料中有很多有趣的物理现象, 例如磁晶各向异性、自旋霍尔效应、拓扑绝缘体等, 都与自旋轨道耦合密切相关. 在表面/界面体系中, 由于结构反演不对称导致的自旋轨道耦合称为Rashba自旋轨道耦合, 它最早在半导体材料中获得研究, 并因其强度可由栅电压灵活调控而备受关注, 成为电控磁性的重要物理基础之一. 继半导体材料后, 金属表面成为具有Rashba自旋轨道耦合作用的又一主流体系. 本文以Au(111), Bi(111), Gd(0001)等为例综述了磁性与非磁性金属表面Rashba自旋轨道耦合的研究进展, 讨论了表面电势梯度、原子序数、表面态波函数的对称性, 以及表面态中轨道杂化等因素对金属表面Rashba自旋轨道耦合强度的影响. 在磁性金属表面, 同时存在Rashba自旋轨道耦合作用与磁交换作用, 通过Rashba自旋轨道耦合可能实现电场对磁性的调控. 最后, 阐述了外加电场和表面吸附等方法对金属表面Rashba自旋轨道耦合的调控. 基于密度泛函理论的第一性原理计算和角分辨光电子能谱测量是金属表面Rashba自旋轨道耦合的两大主要研究方法, 本文综述了这两方面的研究结果, 对金属表面Rashba自旋轨道耦合进行了深入全面的总结和分析.     

Semiconductor electrons in electric and magnetic fields

Optical properties of semiconductors in the simultaneous presence of electric and magnetic fields are reviewed, with particular emphasis on the possibilities of modulation techniques. First, the problem of an electron in crossed and parallel fields is solved in the one-level effective mass approximation (EMA), and the results are used to interpret the experimental interband transitions in Ge, with due account of the degenerate character of the valence band in this material. The limitations of the one-level EMA are discussed, and the two-level model is introduced, which correctly describes the experimentally observed transition from a magnetic type to an electric type of motion in increasing transverse electric field. Possibilities to observe electric field effects in cyclotron resonance transitions are discussed in this approximation. Finally, the three-level model is used to describe properly both orbital and spin properties of conduction electrons. It is demonstrated that in a small-gap semiconductor with large spin-orbit interaction a sufficiently strong transverse electric field destroys the Landau orbital quantization but not the Pauli spin quantization. Possible experimental consequences of this situation are discussed. Influence of finite dimensions of the sample on the character of the electron motion in crossed and parallel fields is examined. A possibility to achieve the semiconductor-semimetal transition in a symmetryinduced zero-gap semiconductor in crossed field configuration is predicted and described, taking into account the Luttinger effects in the magnetic level structure.     

Gate control of quantum dot-based electron spin–orbit qubits

We investigate theoretically the coherent spin dynamics of gate control of quantum dot-based electron spin–orbit qubits subjected to a tilted magnetic field under electric-dipole spin resonance (EDSR). Our results reveal that Rabi oscillation of qubit states can be manipulated electrically based on rapid gate control of SOC strength. The Rabi frequency is strongly dependent on the gate-induced electric field, the strength and orientation of the applied magnetic field. There are two major EDSR mechanisms. One arises from electric field-induced spin–orbit hybridization, and the other arises from magnetic field-induced energy-level crossing. The SOC introduced by the gate-induced electric field allows AC electric fields to drive coherent Rabi oscillations between spin-up and -down states. After the crossing of the energy-levels with the magnetic field, the spin-transfer crossing results in Rabi oscillation irrespective of whether or not the external electric field is present. The spin–orbit qubit is transferred into the orbit qubit. Rabi oscillation is anisotropic and periodic with respect to the tilted and in-plane orientation of the magnetic field originating from the interplay of the SOC, orbital, and Zeeman effects. The strong electrically-controlled SOC strength suggests the possibility for scalable applications of gate-controllable spin–orbit qubits.     

Effect of electric field and magnetic field on spin transport in bilayer graphene armchair nanoribbons: A Monte Carlo simulation study

In this article we study the effect of external magnetic field and electric field on spin transport in bilayer armchair graphene nanoribbons (GNR) by employing semiclassical Monte Carlo approach. We include D'yakonov-Perel' (DP) relaxation due to structural inversion asymmetry (Rashba spin-orbit coupling) and Elliott-Yafet (EY) relaxation to model spin dephasing. In the model we neglect the effect of local magnetic moments due to adatoms and vacancies. We have considered injection polarization along z-direction perpendicular to the plane of graphene and the magnitude of ensemble averaged spin variation is studied along the x-direction which is the transport direction. To the best of our knowledge there has been no theoretical investigation of the effects of external magnetic field on spin transport in graphene nanoribbons. This theoretical investigation is important in order to identify the factors responsible for experimentally observed spin relaxation length in graphene GNRs.     

Generating spin currents in semiconductors with the spin Hall effect

We investigate electrically induced spin currents generated by the spin Hall effect in GaAs structures that distinguish edge effects from spin transport. Using Kerr rotation microscopy to image the spin polarization, we demonstrate that the observed spin accumulation is due to a transverse bulk electron spin current, which can drive spin polarization nearly 40 microns into a region in which there is minimal electric field. Using a model that incorporates the effects of spin drift, we determine the transverse spin drift velocity from the magnetic field dependence of the spin polarization.     

Current-induced spin accumulation in lateral superlattices with Rashba and Dresselhaus spin–orbit interaction

The current-induced spin accumulation is calculated for a 1D lateral semiconductor superlattice with spin–orbit interaction of the Rashba and Dresselhaus type. Due to its particular symmetry, the Rashba interaction alone only leads to an in-plane component of the magnetization transverse to the applied electric field. When in addition a Dresselhaus contribution is present, this symmetry is lifted, and all components of the magnetization are induced by the electric field. Based on the density-matrix approach, the induced spin polarization is determined as a function of external in-plane electric and magnetic fields.     

Tunable Van Hove singularities and the magnetization in a two-dimensional electron gas with the spin–orbit interaction in a parallel magnetic field

The problem of finding the single-particle density of states of a two-dimensional electron gas with the spin–orbit interaction in a parallel magnetic field has been solved. It has been shown that, with increasing field, the square-root singularity of the density of states (N(E) ~ 1 / \(\sqrt {E + 1} \)) existing at the minimum energy in zero magnetic field becomes logarithmic (the Van Hove singularity) and is displaced inside the spectrum, and the minimum energy of the spectrum decreases. The presence of two types of spin–orbit interaction (Rashba and Dresselhaus) is responsible for two peaks of the density of states and for an additional step in the density of states at certain directions of the magnetic field. The energy position of these features can be determined from the magnetization of the electron gas. This makes it possible to find the Rashba and Dresselhaus coupling constants.     

The electric “Meissner effect” in spin superconductor

Spin superconductivity results from the condensation of spin-triplet but charge neutralparticles (e.g., triplet excitons). We present a Laplace-type equation describingelectrostatic properties of spin superconductors. With the phenomenological equationsobtained, we show that there exists an electric “Meissner effect” against the spatialvariation of the electric field along the magnetic moment direction, in particular,(?·?)(?·E). Severaldistinctive characteristics of this electric “Meissner effect” emerge in spinsuperconductors. Firstly, the variation of the electric field(?·?)(?·E) has an abruptdecrease at the boundary, which is analogous to the screen effect for electric fieldE in a uniform dielectric material. Secondly, thesuper-spin current distributes inside or near the boundaries of a spin superconductor,which depends on the magnitude of gradient for the external driven electric field.     

Theoretical investigations on the Stark-Zeeman effect of the 2p~{}^{\mathsf 2}P3/2-level in 6Li for perpendicularly crossed fields

The splitting behaviour of the P_3/2 hyperfine structure levels is investigated in ⁶Li for homogeneous crossed electric and magnetic fields (Stark-Zeeman effect). This is done by diagonalizing the perturbation matrix comprising the hyperfine interaction, the electronic and nuclear magnetic interaction and the effective electric interaction obtained by transforming the quadratic Stark effect to a first order perturbation interaction. Symmetries are used to find analytic formulae for level shifts and crossing points if only one external field is present. A reflection symmetry unbroken with all three interactions present permits the decomposition of the 12 ×12 matrix into two 6 ×6 submatrices. The structure of energy eigenvalue surfaces epsilon_{F,M F}(B,E) of the two subsystems is found by numeric diagonalization of the perturbation matrix and is displayed in the ranges |B|< 1 mT kV/cm. The total angular momentum F = J + I  (J = 3/2, electronic angular momentum, I = 1, nuclear spin) and the magnetic quantum number M_F provide labels for all surfaces. All crossing points of the energy surfaces have been found. Adiabatic level transfer occurring in atoms traversing a sequence of crossed magnetic and electric fields is explained. Berry phases occur for cycles around some crossing points. Their presence or absence is explained.     

52Cr spinor condensate: a biaxial or uniaxial spin nematic

We show that the newly discovered 52Cr Bose condensate in zero magnetic field can be a spin nematic of the following kind: a "maximum" polar state, a "colinear" polar state, or a biaxial nematic ferromagnetic state. We also present the phase diagram with a magnetic field in the interaction subspace containing the chromium condensate. It contains many uniaxial and biaxial spin nematic phases, which often but not always break time reversal symmetry, and can exist with or without spontaneous magnetization.     

Rashba coupling induced spin accumulation in two-dimensional domain wall

Non-equilibrium spin accumulation in two-dimensional domain wall (DW) in the presence of external electric field and Rashba type spin-orbit coupling within the Boltzmann semi-classical model is investigated. Transport and relaxation of spin polarized current in the DW is governed by spin-flip rates which are determined by the Rashba interaction and magnetic impurities. Numerical results show that at low impurity densities and nonadiabatic transport regimes, the Rashba interaction significantly enhances spin polarization of conduction electrons inside the DW.