Zitterbewegung of wave packets and conductance of a quasi-one-dimensional channel in the presence of spin-orbit coupling

The electron energy spectrum and wave functions for a quasi-one-dimensional channel with Rashba spin-orbit coupling are calculated. The dynamics of wave packets in thin wires based on GaAs/In_0.23Ga_0.77As and AlGaAs/GaAs heterostructures with Rashba spin-orbit coupling are studied. Spin polarizations are found. The effect of splitting of wave packets with respect to their centers of mass and Zitterbewegung of their centers are discovered. The characteristics of wave-packet oscillations and spin density for free electrons and under confinement conditions are compared. A method for controlling the conductance of the quasi-one-dimensional channel using a controlling electrode is proposed.     

Dynamics of 2D electron wave packets with different initial spin polarization in 2D structures with spin-orbit coupling

The effect of splitting and zitterbewegung of 2D-electrons wave packets in the presence of Rashba spin-orbit coupling has been investigated. It is shown that nonstandard dynamics of wave packets occurs in the systems where the complete system of eigenfunctions is formed by states with different chirality. The time evolution of wave packets depends on the initial electron spin orientation. It is established that the oscillations of packet centers decay with time. Similar effects were studied by us previously for packets with initial spin orientation perpendicular to the 2D electron gas plane.     

Matter-wave propagation in optical lattices

Coherent propagation of atomic-matter waves in a one-dimensional optical lattice is studied. Wave packets of cold two-level atoms propagate simultaneously in two optical potentials in a dressed-state basis. Three regimes of the wave-packet propagation are specified by the quantity Δ² /ω _D , where Δ and ω _D are the dimensionless atom–laser detuning and the Doppler shift, respectively. At Δ² /ω _D ≫ 1, the propagation is essentially adiabatic, at Δ² /ω _D ≪ 1, it is (almost) resonant, and at Δ² ≃ ω _D , the wave packets propagate nonadiabatically, splitting at each node of the standing wave. The latter means that the atom makes a transition from one potential to the other one when crossing each node, and the probability of that transition is given by a Landau–Zener-like formula. All the regimes of propagation are studied with δ-like and Gaussian wave packets in the momentum and position spaces. Varying the control parameters, we can create wave packets trapped in a well of optical potentials and moving ballistically in a given direction in close analogy with point-like atoms. Within some range of the parameters, we force the atom to move in a pure quamtum-mechanical manner in such a way that a part of the packet is trapped in a well, and the other part propagates ballistically. The propagation modes are found to be characterized by different types of time evolution of the uncertainty product and the Wigner function.     

Maxwell equation for coupled spin-charge wave propagation

We show that the dissipationless spin current in the ground state of the Rashba model gives rise to a reactive coupling between the spin and charge propagation, which is formally identical to the coupling between the electric and the magnetic fields in the (2 + 1)-dimensional Maxwell equation. This analogy leads to a remarkable effect of fractionalization of spin packets (FSP) where a density packet can spontaneously split into two counterpropagation packets, each carrying the opposite spin. In a certain parameter regime, the coupled spin and charge wave propagates like a transverse "photon." We propose both optical and purely electronic experiments to detect the FSP effect.     

Spin Transport in the Presence of Rashba Interaction

A Gaussian type spin-polarized electronic wave packet is constructed to investigate the spin transport behaviour in an infinite two-dimensional electron gas system with Rashba spin--orbit (SO) interaction by solving the Schrödinger equation exactly. In the presence of Rashba SO interaction, the spin-dependent force induces a momentum dependent splitting of the two spin directions, the average spin current indicates the corresponding spin accumulation clearly. Furthermore, the coherence of the injected spin-polarized wave packet, as well as the transverse force, decays during the motion in the Rashba SO regime.     

Diffractive S and D wave vector mesons in deep inelastic scattering

Helicity amplitudes for diffractive leptoproduction of the S and D wave states of vector mesons are derived. A dramatically different spin dependence for production of the S and D wave vector mesons is predicted. It is found that R=σ_L/σ_T is very small and that the higher twist effects in the production of longitudinally polarized D wave vector mesons are abnormally large. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 4, 268–273 (25 February 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Selective Alignment of D2 Induced by Two Ultrashort Laser Pulses

通过求解D₂分子在飞秒激光场中的含时薛定谔方程,研究了室温下D₂分子在超快飞秒激光驱动下的的转动波包动力学. 选择用第一束超短飞秒脉冲与温度为300 K的D₂分子系综相互作用产生一个相干转动波包,用第二束超短飞秒脉冲在波包的1/4和3/4恢复周期选择操纵D₂分子取向. 研究结果表明,通过选择两束超短飞秒脉冲的延迟时间,可以有效控制D₂分子转动波包中奇偶态的相对布居,从而选择性的控制D₂分子取向.     

Diffraction of the wave packet of a three-level Λ atom in the field of a multifrequency standing light wave

The diffraction of the wave packet of a three-level atom in a multifrequency optical radiation field is studied. A new type of coherent beam splitter for atoms that employs the scattering of a wave packet in the field of four standing light waves with different spatial shifts is proposed on this basis. It is shown that this interaction scheme makes it possible to obtain large splittings (>100ℏk) of the wave packet of a three-level Λ atom in momentum space into only two coherent components. In addition, the atoms in these coherent components are in long-lived atomic states, which substantially simplifies the experimental implementation of such a splitter. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 6, 386–391 (25 September 1997)     

Josephson and quasiparticle currents in tunneling junctions between partially dielectrized (partially gapped) superconductors with spin density waves

The current-voltage characteristics (CVC) are calculated for the Josephson, interference, and quasiparticle components of the current through a tunneling junction formed by two superconductors with spin density waves (SDW). The treatment is based on the model of partial dielectrization (gapping) of the Fermi surface and the assumption of pinning of the spin density waves. The following particular cases are studied in detail: asymmetric SDW superconductor-ordinary superconductor junctions and symmetric junctions between two identical SDW superconductors. The positions and nature of the singularities in the CVC are determined. For a symmetric contact the possibility of the existence of asymmetric CVC’s is predicted. The calculations are in qualitative agreement with the experimentally observed behavior of the CVC’s of tunneling junctions and microcontacts containing the SDW superconductor with heavy fermions URu₂Si₂. Fiz. Tverd. Tela (St. Petersburg) 41, 1743–1749 (October 1999)     

PbTe/PbSrTe半导体非对称量子阱中的Rashba效应

窄带隙半导体异质结构的自旋效应最近受到了国际上的很大关注.Ⅳ-Ⅵ族半导体具有各向异性和多能谷的特征,因此可以预期Rashba自旋效应在不同取向的Ⅳ-Ⅵ族半导体量子阱结构中存在显著差异.计算了多个取向的Pb_1-ySr_yTe/PbTe/Pb_1-xSr_xTe非对称量子阱中的Rashba分裂能,结果表明［100］取向的PbTe量子阱的Rashba分裂能在阱宽为5.0nm时 关键词： Ⅳ-Ⅵ族半导体 非对称量子阱 Rashba效应 自旋-轨道耦合分裂     

Motion of an electronic wave packet in an electromagnetic field

An equation is derived for the matrix of the parameters of a small Gaussian wave packet moving in arbitrary fixed electromagnetic fields. The equation can be used to describe the evolution of wave packets in a wide class of vacuum devices. A simple example of the evolution of a packet in a constant magnetic field is studied. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 8, 515–520 (25 October 1996)     

Effect of crystal field on the spin density at the copper nucleus in copper complexes

The role of lower symmetry component of the crystal field in causing a mixing of excited 3d ^x−1 4s with the ground 3d ^x configuration and leading to spin density at the nucleus for iron group ions was suggested by Griffith and Orgel. This mechanism has been examined in detail for the two low-symmetry copper complexes, one square planar (D_4h symmetry) and the other distorted tetrahedron (D_2d symmetry) and the calculation has been performed using the powerful Racah method and tensor operator technique. It is found that for the two types of copper complexes, copper pthalocyanin (square planar, D_4h symmetry) and cesium copper chloride (distorted tetrahedron, D_2d symmetry) the contribution from this mechanism to the spin density at the nucleus vanishes identically.     

Dynamic generation of entangling wave packets in XY spin system with decaying long-range couplings

The dynamic generation of spin entanglement between two distant sites in a XY model with 1/r ² decay long-range couplings was studied. Due to the linear dispersion relation ε(k)∼|k| of magnons in such a model, a well-located spin state can be dynamically split into two moving entangled local wave packets without changing their shapes. Interestingly, when such two wave packets meet at the diametrically opposite site after the fast period τ = Nπ/J, the initial well-located state is completely recurrent. Numerical calculation was performed to confirm the analytical result even if the ring system of sizes N up to several thousands is considered. The truncation approximation for the coupling strengths was also studied. Numerical simulation shows that the above conclusions still hold even if the range of the coupling strength is truncated to a relatively short scale compared with the size of the spin system. Supported by the National Natural Science Foundation of China (Grant Nos. 90203018, 10474104 and 60433050) and the National Fundamental Research Program of China (Grant Nos. 2001CB309310 and 2005CB724508)     

Electronic double refraction due to the Rashba effect: Analytical and numerical results

By analogy with the classic effect of the double refraction of light, we investigate the relevant effect of an electron entering from the Non-Rashba region to the Rashba region in two-dimensional systems. It is shown that the effect of electronic double refraction is determined by a combined parameter γ = m ^* λ _F α/2πħ², rather than both the Rashba coefficient α and wavelength λ _F of a Fermi electron, separately. For the case of normal incidence, the analytical expressions for the wavefunction of the electron are presented; it is predicted that the Rashba spin-orbit coupling can induce a current perpendicular to the normal incident direction of the electron. Moreover, the general case of incident electron with any given momentum and spin state are studied numerically in detail, including the abrupt changes of spin direction and the two-step characters for reflection.      

Application of Boltzmann Equation on Spin Diffusion of Ferromagnetic Superfluid <Superscript>3</Superscript>He: Near Critical Temperature

Different scattering processes of quasiparticles containing a binary process, a coalescence process and a decay process in transition probabilities are taken into account. In the meantime, interaction between Bogoliubov quasiparticles as well as that between normal and superfluid components (spin up-spin down quasiparticles) of ferromagnetic superfluid ³He-A ₁ are considered. Pfitzner procedure is used in the calculation of triplet and singlet quasiparticle scattering amplitude existing in transition probabilities of the collision integral of standard Boltzmann equation at melting pressure. Pfitzner procedure is extended beyond s-p approximation by adding higher angular momentum components. Then, using the results of Boltzmann equation and considering smallness of the gap close to T _c↑, the change of the spin diffusion coefficients tensor of the A ₁-phase of superfluid ³He close to critical temperature and melting pressure is calculated. Temperature dependence of the spin diffusion coefficient change, i.e., δD _xyxy /D⌈=(3/2)(δD _xzxz /D)⌉, is −0.71(1−(T/T _c↑))^1/2. It is also shown that interaction between normal and Bogoliubov quasiparticles (normal-superfluid components interaction) is very important to transport properties such as spin diffusion close to critical temperature. Furthermore, using s-p approximation, the prefactor of δD _xyxy /D is plotted in terms of pressure; hence, the pressure dependence of δD _xyxy /D is also determined.     

Ferromagnetic resonance investigation of nanocrystalline FeCuNbSiB

An elaborate line-shape analysis of the ferromagnetic resonance (FMR) spectra taken in the temperature range 100 K to 350 K on amorphous FeCuNbSiB alloys before and after nanocrystallizing them reveals that in the nanocrystalline state, (i) spin wave stiffness (D) is enhanced while the saturation magnetization,M _S, is reduced, (ii) both the ‘in-plane’ anisotropy field,H _K, as well as the FMR line-width scale with MS, (iii) the single-ion anisotropy of spin-orbit plus crystal field origin dominates over the twoion anisotropy of dipolar origin and (iv) multi-magnon scattering contributions to FMR line-width become important in some cases     

Quantum theory of impurity migration in crystals

A quantum theory of impurity migration in crystals is proposed. The impurity state is taken in the form of a wave packet constructed out of its Bloch states in the host lattice. Its time evolution is studied including its interaction with the host lattice phonons. A correspondence is established between the classical diffusion equation and the time evolution of the probability density arising out of the impurity wave packet. The diffusion coefficient D_T and trapping rate γ_T are related to the imaginary part of the energy shift of the impurity caused by its interaction with phonons. The detailed calculations are carried out using second order perturbation theory for the energy shift. The Debye model for the host lattice and effective mass approximation for the impurity band are used. At low temperature D_T is found to be proportional to_T3/2, and at high temperature the Arrhenius formula of Vineyard is obtained. The estimated migration energy for μ⁺ migration in bcc metals agrees reasonably with the experimental values.     

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.     

Thermoelectric effects in a double-dot Aharonov-Bohm interferometer with Rashba spin-orbit interaction

We investigate the thermoelectric effects in a double-dot Aharonov-Bohm interferometer coupled to ferromagnetic leads held at different temperatures. The interplay of Rashba spin-orbit interaction (RSOI) and magnetic flux ϕ induces various interesting spin-dependent interference phenomena. The thermoelectric transport oscillates with ϕ. The peak of the thermopower S and figure of merit ZT splits into two new peaks and its splitting increases with the Rashba induced phase factor φ _R . With increasing φ _R S and ZT at ϕ = ± 2nπ (n = 0,1,2,...) exhibit a conversion from a peak to a valley. In the presence of the interplay of RSOI and ϕ by increasing spin polarization the splitting peaks of S (ZT) become asymmetric and ZT is greatly enhanced. The influence of the quantum dot levels on thermoelectric effects is also analyzed.     

Spin current and its heat effect in a multichannel quantum wire with Rashba spinben orbit coupling

Using the perturbation method, we theoretically study the spin current and its heat effect in a multichannel quantum wire with Rashba spin—orbit coupling. The heat generated by the spin current is calculated. With the increase of the width of the quantum wire, the spin current and the heat generated both exhibit period oscillations with equal amplitudes. When the quantum-channel number is doubled, the oscillation periods of the spin current and of the heat generated both decrease by a factor of 2. For the spin current j_s,xy, the amplitude increases with the decrease of the quantum channel; while the amplitude of the spin current j_s,yx remains the same. Therefore we conclude that the effect of the quantum-channel number on the spin current j_s,xy is greater than that on the spin current j_s,yx. The strength of the Rashba spin—orbit coupling is tunable by the gate voltage, and the gate voltage can be varied experimentally, which implies a new method of detecting the spin current. In addition, we can control the amplitude and the oscillation period of the spin current by controlling the number of the quantum channels. All these characteristics of the spin current will be very important for detecting and controlling the spin current, and especially for designing new spintronic devices in the future.