Bychkov Rashba Research Articles

Theory of spin–charge-coupled transport in proximitized graphene: an SO(5) algebraic approach

Establishing the conditions under which orbital, spin and lattice-pseudospin degrees of freedom are mutually coupled in realistic nonequilibrium conditions is a major goal in the emergent field of graphene spintronics. Here, we use linear-response theory to obtain a unified microscopic description of spin dynamics and coupled spin–charge transport in graphene with an interface-induced Bychkov–Rashba effect. Our method makes use of an SO(5) extension of the familiar inverse-diffuson approach to obtain a quantum kinetic equation for the single-particle density matrix that treats spin and pseudospin on equal footing and is valid for arbitrary external perturbations. As an application of the formalism, we derive a complete set of drift–diffusion equations for proximitized graphene with scalar impurities in the presence of electric and spin-injection fields which vary slowly in space and time. Our approach is amenable to a wide variety of generalizations, including the study of coupled spin–charge dynamics in layered materials with strong spin–valley coupling and spin–orbit torques in van der Waals heterostructures.

Optical properties of a two-dimensional GaAs quantum dot under strain and magnetic field

It is well known that the use of the strain plays an important role in the material properties. Strain effect is a potential tool for altering the atomic positions and defect formations. It can adjust the electronic structures and lattice vibrations. It can also affect the phase transition of the structure, the physical and chemical properties. Consequently, in this paper, we have studied the effects of strain and magnetic field on optical properties of a two-dimensional quantum dot. The Hamiltonian of our system consists of the Bychkov–Rashba, Dresselhaus and strain-dependent terms. Using the diagonalization method, we have obtained the energy levels and wave functions of the system and thereby the refractive index changes and absorption coefficient in the presence of different strains. According to the results, it is found that an anti-crossing magnetic field is 7.37 T and it does not depend on the strain. Also, the energy transition increases with enhancement in the strain and decreases with increase in the magnetic field. The refractive index changes and absorption coefficient shifts toward lower (higher) energies for negative (positive) strain. The energy transition has lower values for negative strain at fixed magnetic field and confinement length.

Strain effect on the third-harmonic generation of a two-dimensional GaAs quantum dot in the presence of magnetic field and spin–orbit interaction

The strain effect on the third-harmonic generation (THG) of a two-dimensional GaAs quantum dot has been investigated within the effective mass approximation. For this purpose, first, we have calculated the energy levels and wave function of the system in the presence of Bychkov–Rashba and Dresselhaus terms and strain-dependent term by accomplish the diagonalization method. Then we have computed the THG by an analytical expression. The results illustrate that: (1) there is a maximum in TGH for a special magnetic field corresponding to the anti-crossing magnetic field (Bac). (2) The Bac is not depended on the strain. (3) There is a minimum in TGH at special strain, and we can control the THG by strain and magnetic field.

Bound State of an Electron in a MOS Structure Due to the Spin–Orbit Interaction

It is shown that two electrons situated in a quantum well near a metallic electrode are attracted to each other due to the Bychkov–Rashba spin–orbit interaction (SOI) and electrostatic image forces. For quite accessible values of the characteristic parameters of the system, the effective attraction due to the SOI dominates over the Coulomb repulsion, and the formation of a bielectron becomes possible. The theory of the effect is especially simple and clear in the case of a quantum wire. The binding energy of the electron pair significantly increases under the application of a gate voltage of appropriate polarity.

Strain effect on the spin relaxation rate of a two-dimensional GaAs quantum dot

The strain effect on the spin relaxation rate of a two-dimensional GaAs quantum dot has been investigated within the effective mass approximation. For this purpose, first we have calculated the energy levels and wave functions of the system in the presence of Bychkov–Rashba and Dresselhaus terms and strain-dependent term by using the diagonalization method. Then, we have computed the spin relaxation rate by Fermi’s Golden rule. The results show that: (i) there is a maximum in spin relaxation rate for a special magnetic field, that is corresponding to the anti-crossing magnetic field (Bac). (ii) The Bac does not depend on the strain. (iii) There is a minimum in spin relaxation rate at the special strain.

Effects of strain, magnetic field and temperature on entropy of a two dimensional GaAs quantum dot under spin–orbit interaction

In this paper, we have studied the effects of temperature, strain and magnetic field on non-extensive entropy of a two-dimensional (2D) quantum dot under spin–orbit interaction. To this end, we have obtained the energy levels and wave functions of the system in the presence of Bychkov–Rashba, Dresselhaus and strain effects by using diagonalization procedure. Then, we have used the Tsallis formalism and calculated the entropy of the system. It is found that the entropy is increased with enhancing the temperature with and without strain. The entropy increases with considering the negative strain. The strain has not strongly effect on the entropy at low temperatures.

Bielectron Formed in a 2D System by the Spin–Orbit Interaction and Image Forces

It has been shown that two electrons situated in a quantum well near a metallic electrode attract each other owing to the Bychkov–Rashba spin–orbit interaction (SOI) and by electrostatic image forces. It has been shown within a simple model that the SOI-induced effective attraction is stronger than the Coulomb repulsion and the formation of a bielectron becomes possible at quite accessible values of the characteristic parameters of the system.

Pressure effects on crystal and electronic structure of bismuth tellurohalides

We study the possibility of pressure-induced transitions from a normal semiconductor to a topological insulator (TI) in bismuth tellurohalides using density functional theory and tight-binding method. In BiTeI this transition is realized through the formation of an intermediate phase, a Weyl semimetal, that leads to modification of surface state dispersions. In the topologically trivial phase, the surface states exhibit a Bychkov–Rashba type dispersion. The Weyl semimetal phase exists in a narrow pressure interval of 0.2 GPa. After the Weyl semimetal–TI transition occurs, the surface electronic structure is characterized by gapless states with linear dispersion. The peculiarities of the surface states modification under pressure depend on the band-bending effect. We have also calculated the frequencies of Raman active modes for BiTeI in the proposed high-pressure crystal phases in order to compare them with available experimental data. Unlike BiTeI, in BiTeBr and BiTeCl the topological phase transition does not occur. In BiTeBr, the crystal structure changes with pressure but the phase remains a trivial one. However, the transition appears to be possible if the low-pressure crystal structure is retained. In BiTeCl under pressure, the topological phase does not appear up to 18 GPa due to a relatively large band gap width in this compound.

General solution of the Dirac equation for quasi-two-dimensional electrons

The general solution of the Dirac equation for quasi-two-dimensional electrons confined in an asymmetric quantum well, is found. The energy spectrum of such a system is exactly calculated using special unitary operator and is shown to depend on the electron spin polarization. This solution contains free parameters, whose variation continuously transforms one known particular solution into another. As an example, two different cases are considered in detail: electron in a deep and in a strongly asymmetric shallow quantum well. The effective mass renormalized by relativistic corrections and Bychkov–Rashba coefficients are analytically obtained for both cases. It is demonstrated that the general solution transforms to the particular solutions, found previously (Eremko et al., 2015) with the use of spin invariants. The general solution allows to establish conditions at which a specific (accompanied or non-accompanied by Rashba splitting) spin state can be realized. These results can prompt the ways to control the spin degree of freedom via the synthesis of spintronic heterostructures with the required properties.

Exchange interaction between magnetic impurities on surfaces of CuxPd1−x and CuxAu1−x random substitutional alloys

We present fully relativistic first principles calculations of the exchange interactions between magnetic impurities deposited on the (1 1 1) surfaces of CuxPd1−x and CuxAu1−x random substitutional alloys, described using the coherent potential approximation. We show that as with pure surfaces of Cu and Au, where Shockley-type surface states mediate an RKKY-type interaction, a surface state and its dispersion can be obtained from studying the Bloch spectral function. In the second part of the paper we show how the details of the interaction are determined by the properties and dispersion of the surface states of the host material. We find an extra exponential decay in the range of the interactions compared to the 1/R2 decay on surfaces of pure metals. The similar topology of the Fermi surface of Cu and Au allows us to scale the spin–orbit coupling and to study the Bychkov–Rashba splitting. Alternatively, the entirely different topology of the Cu and Pd Fermi surfaces allows us to study changes in the surface-state dispersion of the RKKY interaction between surface impurities.

Thermal entanglement of electronic spin–subband in a Rashba isotropic two-dimensional nanodot

In the present report the thermal entanglement between electronic spin and subband states in a Rashba isotropic nanodot, under the action of a perpendicular magnetic field, is investigated. The nanodot is assumed to be in thermal equilibrium with a heat reservoir so that all electronic micro states (subbands plus spin states) with definite probabilities participate into the entanglement. Introducing a Casimir operator, C^, which commutes with the total Hamiltonian, it is shown that the Hamiltonian is block-diagonal, each of dimensions 2Ne+1, where Ne is an eigenvalue of C^. We then proceed to diagonalize each block so that the thermal (Gibb’s) density matrix, written in the bases of the total Hamiltonian, becomes block-diagonal as well. Consequently, a simple procedure to calculate the negativity, as a measure of thermal entanglement is developed. Our calculations show that the ground state of the combined system is an entangled one whose degree depends upon the externally controllable magnetic field and the Bychkov–Rashba (BR) parameter. Moreover, the thermal spin–subband entanglement exhibits a local minimum followed by a local maximum and asymptotically vanishes as the temperature is increased. The variation of the extrema as well as the rate at which the entanglement approaches zero, with the magnetic field and BR parameter are also discussed.

Spin-orbit-interaction induced singularity of the charge density relaxation propagator

The charge density relaxation propagator of a two dimensional electron system, which is the slope of the imaginary part of the polarization function, exhibits singularities for bosonic momenta having the order of the spin-orbit momentum and depending on the momentum orientation. We have provided an intuitive understanding for this non-analytic behavior in terms of the inter chirality subband electronic transitions, induced by the combined action of Bychkov-Rashba (BR) and Dresselhaus (D) spin-orbit coupling. It is shown that the regular behavior of the relaxation propagator is recovered in the presence of only one BR or D spin-orbit field or for spin-orbit interaction with equal BR and D coupling strengths. This creates a new possibility to influence carrier relaxation properties by means of an applied electric field.

Theory and model analysis of spin relaxation time in graphene - Could it be used for spintronics?

Graphene appears to be an excellent candidate for spintronics due to the low spin–orbit coupling in carbon, the two-dimensional nature of the graphene sheet, and the high electron mobility. However, recent experiments by Tombros et al. [Nature 448, 571 (2007).] found a prohibitively short spin-decoherence time in graphene. We present a comprehensive theory of spin decoherence in graphene including intrinsic, Bychkov–Rashba, and ripple related spin–orbit coupling. We find that the available experimental data can be explained by an intrinsic spin–orbit coupling which is orders of magnitude larger than predicted in first principles calculations. We show that comparably large values are present for structurally and electronically similar systems, MgB2 and Li intercalated graphite. The spin-relaxation in graphene is neither due to the Elliott–Yafet nor due to the Dyakonov–Perel mechanism but a smooth crossover between the two regimes occurs near the Dirac point as a function of the chemical potential.

Beating of Friedel oscillations induced by spin-orbit interaction

By exploiting our recently derived exact formula for the Lindhard polarization function in the presence of Bychkov-Rashba (BR) and Dresselhaus (D) spin-orbit interaction (SOI), we show that the interplay of different SOI mechanisms induces highly anisotropic modifications of the static dielectric function. We find that under certain circumstances the polarization function exhibits doubly-singular behavior, which leads to an intriguing novel phenomenon, beating of Friedel oscillations. This effect is a general feature of systems with BR+D SOI and should be observed in structures with a sufficiently strong SOI.

Interaction of branches of magnetoplasmon spectrum in 2D systems with spin–orbit coupling

We have theoretically investigated magnetoplasma oscillations of a 2D electronic system with spin–orbit interaction (SOI) in the Bychkov–Rashba model. Accounting for SOI results in new branches of magnetoplasmons as compared with the spinless case where the Bernstein modes exist only. A remarkable feature of the problem in question is magnetic field controlled interaction of branches (multiple anticrossings). This is manifested in the spectra of plasmon absorption of electromagnetic radiation.

Microwave electric field induced spin transitions of AlAs 2D electrons

We present the first direct electron spin resonance (ESR) on a 2D electron gas in a III – V semiconductor. ESR on a high mobility 2D electron gas in a single AlAs quantum well reveals an electronic g -factor of 1.991 at 9.35 GHz and 1.989 at 34 GHz with a minimal linewidth of 7 Gauss. Both the signal amplitude and its dependence on the position and orientation of the sample in the cavity unambiguously demonstrate that the spin transitions in our experiment are caused by the microwave electric field. We present a model that ascribes the spin transitions to the effective magnetic field acting on the electron spins that arises from (Bychkov–Rashba) spin-orbit interaction and the modulation of the electron wavevector around k F induced by the microwave electric field.

Spin Properties of Electrons in Low-Dimensional SiGe Structures

Using ESR, we investigate g-factor and spin coherence time τ of electrons confined in 2D Si1−xGex {channels} (x 0.2 and in SiGe quantum dots grown on prepatterned Si substrates. The quantum wells exhibit 2D-anisotropy of both g and τ which can be explained in terms of the Bychkov–Rashba field. The latter increases with increasing Ge content in the well indicating that the increasing spin-orbit coupling is more important than interface properties. The narrow ESR permits selective spin manipulation already for x > 0.02. Large, regular arrays of Ge quantum dots (about 109) were grown on prepatterned substrates. Strain in the Si capping layer lowers the conduction band relative to that of Ge causing confinement. The g-shift observed implies the possibility of g-tuning by confinement. The line width shows substantial inhomogeneous broadening whereas the longitudinal spin lifetime is hardly changed with respect to 2D structures.

Anisotropy of g-factor and electron spin resonance linewidth in modulation doped SiGe quantum wells

We investigate the electron spin resonance of electrons in Si1−xGex quantum wells defined by SiGe barriers (19%–25%Ge). Adding small amounts of Ge changes both g-factor and linewidth and their anisotropy. We explain these effects in terms of the Bychkov–Rashba field that originates from one-sided modulation doping. The main effect arises from the increase in spin–orbit interaction with increasing x. We argue that these effects may be used to tune the g-factor of electrons in quantum dots for a selective spin manipulation.

Spin relaxation of 2D electron in Si/SiGe quantum well suppressed by applied magnetic field

We investigate spin resonance of two-dimensional (2D) conduction electrons in a modulation-doped SiGe/Si/SiGe quantum well structure. We find spin relaxation times of the order of microseconds and a 2D anisotropy of both the line broadening (dephasing time) and of the longitudinal spin relaxation. The spin relaxation is dominated by the D'yakonov–Perel spin relaxation mechanism originating from the Bychkov–Rashba spin–orbit field. We find evidence that for high mobility samples the cyclotron motion causes an additional modulation of spin–orbit coupling which leads to an effective reduction of the spin relaxation. For 2D electrons the dependence of the cyclotron frequency on the direction of applied field causes the observed anisotropy of spin relaxation.

BYCHKOV–RASHBA SPLITTING IN INVERSION LAYERS ON HEAVILY-DOPED p-HgCdTe

The Bychkov–Rashba effect in metal–insulator–semiconductor (MIS) structures based on zero-gap HgCdTe with different doping level is investigated experimentally and theoretically. The relative difference between electron concentration in different spin-orbit split sub-subband increases with doping and reaches high values as Δn/n~0,5 at NA-ND~1018 cm-3. Contrary to low-doped HgCdTe the splitting, in the samples investigated, exhibits strong concentration dependence in the wide concentration region.