Efficient spin filtering in a disordered semiconductor superlattice in the presence of Dresselhaus spin-orbit coupling

The influence of the Dresselhaus spin-orbit coupling on spin polarization by tunneling through a disordered semiconductor superlattice was investigated. The Dresselhaus spin-orbit coupling causes the spin polarization of the electron due to transmission possibilities difference between spin up and spin down electrons. The electron tunneling through a zinc-blende semiconductor superlattice with InAs and GaAs layers and two variable distance In_xGa_(1−x)As impurity layers was studied. One hundred percent spin polarization was obtained by optimizing the distance between two impurity layers and impurity percent in disordered layers in the presence of Dresselhaus spin-orbit coupling. In addition, the electron transmission probability through the mentioned superlattice is too much near to one and an efficient spin filtering was recommended.     

Particular nanowire superlattice as a spin filter

A nanowire superlattice of InAs and GaAs layers with In_0.47Ga_0.53As as the impure layers is proposed. The oft-neglected k³ Dresselhaus spin-orbit coupling causes the spin polarization of the electron but often can produce a limited spin polarization. In this nanowire superlattice, Dresselhaus term produce complete spin filtering by optimizing the distance between the In_0.47Ga_0.53As layers and the Indium (In) in the impure layers. The proposed structure is an optimized nanowire superlattice that can efficiently filter any component of electron spins according to its energy. In fact, this nanowire superlattice is an energy dependent spin filter structure.     

Dresselhaus spin-orbit coupling induced spin-polarization and resonance-split in n-well semiconductor superlattices

Using the transfer matrix method, we investigate the electron transmission over multiple-well semiconductor superlattices with Dresselhaus spin-orbit coupling in the potential-well regions. The superlattice structure enhances the effect of spin polarization in the transmission spectrum. The minibands of multiple-well superlattices for electrons with different spin can be completely separated at the low incident energy, leading to the 100% spin polarization in a broad energy windows, which may be an effective scheme for realizing spin filtering. Moreover, for the transmission over n-quantum-well, it is observed that the resonance peaks in the minibands split into n-folds or (n−1)-folds depending on the well-width and barrier-thickness, which is different from the case of tunneling through n-barrier structure.     

Electron spin precession in two-dimensional electron gas with Rashba spin-orbit coupling

Using the time-dependent Schrödinger equation, we present the analytical result of the expectation value of spin injected into a two-dimensional electron gas with respect to an arbitrarily spin-polarized electron state and monitor the spin time-evolution. We demonstrate that the expectation value of spin operator Sx is the time-independent, and only the expectation values in the Sy-Sz plane are time-dependent. A detailed study of spin precession in the spin-valve and spin-transistor geometry is presented, in which the initial spin-polarized electron state point perpendicular and parallel to the current direction, respectively. We put forward the possible reason that the resistance change is independent of gate voltage in the spin-valve geometry. Furthermore, it has been shown that the effective magnetic field generated by the spin-orbit interaction is not same with the truly magnetic field. The main effect of the truly magnetic field is to align the spin along the field direction, but the effective magnetic field generated by the spin-orbit interaction does not.     

Current-induced spin polarization and the spin Hall effect: A quasiclassical approach

The quasiclassical Green function formalism is used to describe charge and spin dynamics in the presence of spin-orbit coupling. We review the results obtained for the spin Hall effect on restricted geometries. The role of boundaries is discussed in the framework of spin diffusion equations.     

Electric tunable of electron spin polarization in hybrid magnetic-electric barrier structures

Electron spin-dependent transport properties have been theoretically investigated in two-dimensional electron gas (2DEG) modulated by the magnetic field generated by a pair of anti-parallel magnetization ferromagnetic metal stripes and the electrostatic potential provided by a normal metal Schottky stripe. It is shown that the energy positions of the spin-polarization extremes and the width of relative spin conductance excess plateau could be significantly manipulated by the electrostatic potential strength and width, as well as its position relative to the FM stripes. These interesting features are believed useful for designing the electric voltage controlled spin filters.     

Spin-orbit gauge and quantum spin Hall effect

We have shown that the non-Abelian spin-orbit gauge field strength of the Rashba and Dresselhaus interactions, when split into two Abelian field strengths, the Hamiltonian of the system can be re-expressed as a Landau level problem with a particular relation between the two coupling parameters. The quantum levels are created with up and down spins with opposite chirality and leads to the quantum spin Hall effect.     

Vertex correction of the anisotropic magnetic impurities to the spin polarization of 2D electron gas

In terms of Kubo's formula and Green's function method, for the two-dimensional electron gas (2DEG) with Rashba spin-orbit coupling (SOC), we study the spin polarization due to the effect from magnetic impurities with anisotropic spin dependent delta type coupling to electrons when an external dc electric field in plane is applied. The vertex correction of impurities in ladder approximation is carried out in the limit of EF?1/τ, Δ. We find that the strength of spin polarization can be significantly modified by vertex correction and the spin polarization is relevant to the anisotropy coefficient γ, but the direction of net spin polarization cannot be changed.     

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.     

Spin filtering in a nonuniform quantum wire with Rashba spin-orbit interaction

We investigate theoretically the spin-polarized electron transport for a wide-narrow-wide (WNW) quantum wire under the modulation of Rashba spin-orbit interaction (SOI). The influence of both the structure of the quantum wire and the interference between different pairs of subbands on the spin-polarized electron transport is taken into account simultaneously via the spin-resolved lattice Green function method. It is found that a very large vertical spin-polarized current can be generated by the SOI-induced effective magnetic field at the structure-induced Fano resonance even in the presence of strong disorder. Furthermore, the magnitude of the spin polarization can be tuned by the Rashba SOI strength and structural parameters. Those results may provide an effective way to design a spin filter device without containing any magnetic materials or applying a magnetic field.     

The effects of Mn concentration on spin-polarized transport through ZnSe/ZnMnSe/ZnSe heterostructures

We have studied the effects of Mn concentration on the ballistic spin-polarized transport through diluted magnetic semiconductor heterostructures with a single paramagnetic layer. Using a fitted function for zero-field conduction band offset based on the experimental data, we found that the spin current densities strongly depend on the Mn concentration. The magnitude as well as the sign of the electron-spin polarization and the tunnel magnetoresistance can be tuned by varying the Mn concentration, the width of the paramagnetic layer, and the external magnetic field. By an appropriate choice of the Mn concentration and the width of the paramagnetic layer, the degree of spin polarization for the output current can reach 100% and the device can be used as a spin filter.     

Spin-polarized transport in one-dimensional waveguide structures with spatially-periodic electronic and magnetic fields

We investigate theoretically the spin-polarized transport in one-dimensional waveguide structure with spatially-periodic electronic and magnetic fields. The interplay of the spin-orbit interaction and in-plane magnetic field significantly modifies the spin-dependent transmission and the spin polarization. The in-plane magnetic fields increase the strength of the Rashba spin-orbit coupling effect for the electric fields along y axis and decrease this effect for reversing the electric fields, even counteract the Rashba spin-orbit coupling effect. It is very interesting to find that we may deduce the strength of the Rashba effect through this phenomenon.     

Electron-spin polarization in a non-magnetic heterostructure

The spin dependent electron transmission through a non-magnetic III-V semiconductor symmetric well is studied theoretically so as to investigate the output transmission current polarization at zero magnetic field. Transparency of electron transmission is calculated as a function of electron energy as well as the well width, within the one electron band approximation along with the spin-orbit interaction. Enhanced spin-polarized resonant tunneling in the heterostructure due to Dresselhaus and Rashba spin-orbit coupling induced splitting of the resonant level is observed. We predict that a spin-polarized current spontaneously emerges in this heterostructure. This effect could be employed in the fabrication of spin filters, spin injectors and detectors based on non-magnetic semiconductors.     

Influence of impurity-induced spin-orbit scattering on persistent spin helix

The persistent spin helix discovered in intrinsic spin-orbit coupled systems previously is reexamined using the motion equations of Green's functions by considering the effect of extrinsic impurity-induced spin-orbit coupling. We find both the intrinsic and extrinsic spin-orbit couplings can increase the excitation energy of spin helix. They together can reduce drastically the lifetime of the spin helix, making it severely departure from the ideal infinite value. The effect of impurity density on spin helix is also analyzed. The results may be helpful to understand experimental measurements on spin helix.     

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.     

Spin-polarized transport in ferromagnet/Rashba quantum dot/ferromagnet system

The transport properties of the Datta and Das's spin transistor with the center normal region (or the quantum dot) having Rashba spin–orbit interaction and electron–electron (e–e) interaction U are investigated. We find while intra-dot level is near or above the chemical potential of the leads, the modulation efficiency of this spin transistor almost is not influenced by U. On the other hand, when the level is below the chemical potential, e–e interaction U may affect the modulator efficiency, because in this case the existence of e–e interaction can change the transport properties of the quantum dot. But the modulation efficiency still keep enough large and the spin transistor can effectively work.     

Non-Abelian hydrodynamics and the flow of spin in spin-orbit coupled substances

Motivated by the heavy ion collision experiments there is much activity in studying the hydrodynamical properties of non-Abelian (quark-gluon) plasmas. A major question is how to deal with color currents. Although not widely appreciated, quite similar issues arise in condensed matter physics in the context of the transport of spins in the presence of spin-orbit coupling. The key insight is that the Pauli Hamiltonian governing the leading relativistic corrections in condensed matter systems can be rewritten in a language of SU(2) covariant derivatives where the role of the non-Abelian gauge fields is taken by the physical electromagnetic fields: the Pauli system can be viewed as Yang-Mills quantum-mechanics in a ‘fixed frame’, and it can be viewed as an ‘analogous system’ for non-Abelian transport in the same spirit as Volovik’s identification of the He superfluids as analogies for quantum fields in curved space time. We take a similar perspective as Jackiw and coworkers in their recent study of non-Abelian hydrodynamics, twisting the interpretation into the ‘fixed frame’ context, to find out what this means for spin transport in condensed matter systems. We present an extension of Jackiw’s scheme: non-Abelian hydrodynamical currents can be factored in a ‘non-coherent’ classical part, and a coherent part requiring macroscopic non-Abelian quantum entanglement. Hereby it becomes particularly manifest that non-Abelian fluid flow is a much richer affair than familiar hydrodynamics, and this permits us to classify the various spin transport phenomena in condensed matter physics in an unifying framework. The “particle based hydrodynamics” of Jackiw et al. is recognized as the high temperature spin transport associated with semiconductor spintronics. In this context the absence of faithful hydrodynamics is well known, but in our formulation it is directly associated with the fact that the covariant conservation of non-Abelian currents turns into a disastrous non-conservation of the incoherent spin currents of the high temperature limit. We analyze the quantum-mechanical single particle currents of relevance to mesoscopic transport with as highlight the Ahronov-Casher effect, where we demonstrate that the intricacies of the non-Abelian transport render this effect to be much more fragile than its abelian analog, the Ahronov-Bohm effect. We subsequently focus on spin flows protected by order parameters. At present there is much interest in multiferroics where non-collinear magnetic order triggers macroscopic electric polarization via the spin-orbit coupling. We identify this to be a peculiarity of coherent non-Abelian hydrodynamics: although there is no net particle transport, the spin entanglement is transported in these magnets and the coherent spin ‘super’ current in turn translates into electric fields with the bonus that due to the requirement of single valuedness of the magnetic order parameter a true hydrodynamics is restored. Finally, ‘fixed-frame’ coherent non-Abelian transport comes to its full glory in spin-orbit coupled ‘spin superfluids’, and we demonstrate a new effect: the trapping of electrical line charge being a fixed frame, non-Abelian analog of the familiar magnetic flux trapping by normal superconductors. The only known physical examples of such spin superfluids are the ³He A- and B-phase where unfortunately the spin-orbit coupling is so weak that it appears impossible to observe these effects.     

Electronic Transport through a Waveguide in the Presence of a Magnetic Obstacle

By means of the transfer matrix technique, the electronic transport through a quantum waveguide in the presence of a magnetic obstacle is investigated theoretically. By comparing the calculated conductance spectra of the opposite spin electrons, we find that there exists a notable spin filtering window in the low energy region. Dependences of such a spin filtering window on the size, position and potential strength of the magnetic obstacle are studied in detail.     

Effect of external magnetic field on superconducting and spin density wave gaps of high-Tc superconductors

A theoretical model is addressed here to study the interplay of the superconductivity (SC) and the spin density wave (SDW) long range orders in underdoped region in the vicinity of on-set of superconductivity in presence of an external magnetic field. The order parameters are calculated by using Zubarev’s technique of Green’s functions and determined numerically self-consistently. The gap parameters are found to be strongly coupled to each other through their coupling constants. The interplay displays BCS type two gaps in the quasi-particle density of states (DOS) which resemble the tunneling conductance of STM experiments. The gap edges in the DOS appear at ±(z+z₁)$\pm (z+z_1)$ and ±(z-z₁)$\pm (z-z_1)$. The applied magnetic field further induces Zeeman splitting which is explained on the basis of spin-filter effect of tunneling experiment.