Rashba Hamiltonian Research Articles

Universal semiclassical equations based on the quantum metric for a two-band system

We derive semiclassical equations of motion for an accelerated wavepacket in a two-band system. We show that these equations can be formulated in terms of the static band geometry described by the quantum metric. We consider the specific cases of the Rashba Hamiltonian with and without a Zeeman term. The semiclassical trajectories are in full agreement with the ones found by solving the Schr\"odinger equation. This formalism successfully describes the adiabatic limit and the anomalous Hall effect traditionally attributed to Berry curvature. It also describes the opposite limit of coherent band superposition giving rise to a spatially oscillating Zitterbewegung motion. At $k=0$, such wavepacket exhibits a circular trajectory in real space, with its radius given by the square root of the quantum metric. This quantity appears as a universal length scale, providing a geometrical origin of the Compton wavelength.

Point-like perturbation of Rashba Hamiltonian

Quantum system with spin–orbit interaction in three-dimensional space is considered. Point-like perturbation for Rashba Hamiltonian is constructed in the framework of the theory of self-adjoint extensions of symmetric operators. Boundary triplet approach is used. The Weyl function and the scattering matrix are constructed.

Point-Like Rashba Interactions as Singular Self-Adjoint Extensions of the Schrödinger Operator in One Dimension

We consider singular self-adjoint extensions for the Schr\{o}dinger operator of spin-$1/2$ particle in one dimension. The corresponding boundary conditions at a singular point are obtained. There are boundary conditions with the spin-flip mechanism, i.e. for these point-like interactions the spin operator does not commute with the Hamiltonian. One of these extensions is the analog of zero-range $\delta$-potential. The other one is the analog of so called $\delta^{(1)}$-interaction. We show that in physical terms such contact interactions can be identified as the point-like analogues of Rashba Hamiltonian (spin-momentum coupling) due to material heterogeneity of different types. The dependence of the transmissivity of some simple devices on the strength of the Rashba coupling parameter is discussed. Additionally, we show how these boundary conditions can be obtained in the non-relativistic limit of Dirac Hamiltonian.

Spin filtering via resonant reflection of relativistic surface states

A microscopic approach is developed to scattering of surface states from a non-magnetic linear defect at a surface with strong spin-orbit interaction. Spin-selective reflection resonances in scattering of Rashba-split surface states by an atomic stripe are theoretically discovered in a proof-of-principle calculation for a model crystal potential. Spin-filtering properties of such linear defects are analyzed within an envelope-function formalism for a perturbed surface based on the Rashba Hamiltonian. The continuous Rashba model is found to be in full accord with the microscopic theory, which reveals the essential physics behind the scattering resonance. The spin-dependent reflection suggests a novel mechanism to manipulate spins on the nanoscale.

Correlation Dimension in Two-Dimensional Disordered Systems with Rashba Spin-Orbit Coupling

The metal-insulator phase transition that arises in the Integer Quantum Hall Effect has been characterized through the multifractal nature of extended states near the center of the Lowest Landau Level. In this work, we obtain numerical solutions for the one-electron Hamiltonian with disorder, where the correlation dimension of extended states in the first two Landau Levels is obtained, by taking into account the Rashba spin-orbit coupling in the Hamiltonian. Although, spin-orbit coupling at moderate field intensities has been determined experimentally, there is no theoretical evidence for the nature of the transition in this case. The correlation dimension of extended states for the resolved spin levels is obtained, and within the statistical error, it is found that the Rashba Hamiltonian in presence of disorder, belongs to the same universality class of spin unresolved systems.

Rashba realization: Raman with RF

We theoretically explore a Rashba spin–orbit coupling scheme which operates entirely in the absolute ground state manifold of an alkali atom, thereby minimizing all inelastic processes. An energy gap between ground eigenstates of the proposed coupling can be continuously opened or closed by modifying laser polarizations. Our technique uses far-detuned ‘Raman’ laser coupling to create the Rashba potential, which has the benefit of low spontaneous emission rates. At these detunings, the Raman matrix elements that link mF magnetic sublevel quantum numbers separated by two are also suppressed. These matrix elements are necessary to produce the Rashba Hamiltonian within a single total angular momentum f manifold. However, the far-detuned Raman couplings can link the three XYZ states familiar to quantum chemistry, which possess the necessary connectivity to realize the Rashba potential. We show that these XYZ states are essentially the hyperfine spin eigenstates of dressed by a strong radio-frequency magnetic field.

Rashba-coupling modelling for two-dimensional and high-order Rashba Hamiltonian for one-dimensional confined heavy holes

Based on the standard multiband Hamiltonian, we have deduced an explicit analytical expression for the Rashba-coupling parameter which clarifies its anomalous behavior for heavy holes , gated in quasi–two-dimensional (Q2D) systems, by letting the density grow. Our modelling agrees remarkably better with experimental results in comparison with earlier theoretical models, while it recovers the expected cubic dependence on the quasi-momentum. For quasi–one-dimensional (Q1D) hh systems, we have formally derived an effective Rashba Hamiltonian with two competitive terms on the quasi-momentum, a linear term and a cubic one as predicted from suitable approximations to the Q2D scope. The Rashba-coupling parameters also behave anomalously and qualitatively support recent experiments in core/shell nanowires. Furthermore, they exhibit an essential asymptotic discontinuity in the low-density regime as a function of the lateral confinement length. For hh, we present closed schemes to accurately quote the Rashba-coupling parameters both for the Q2D and Q1D systems, which become unprecedented for holes.

Strongly anisotropic spin-orbit splitting in a two-dimensional electron gas

Near-surface two-dimensional electron gases on the topological insulator Bi$_2$Te$_2$Se are induced by electron doping and studied by angle-resolved photoemission spectroscopy. A pronounced spin-orbit splitting is observed for these states. The $k$-dependent splitting is strongly anisotropic to a degree where a large splitting ($\approx 0.06$ \AA$^{-1}$) can be found in the $\bar{\Gamma}\bar{M}$ direction while the states are hardly split along $\bar{\Gamma}\bar{K}$. The direction of the anisotropy is found to be qualitatively inconsistent with results expected for a third-order anisotropic Rashba Hamiltonian. However, a $\mathbf{k} \cdot \mathbf{p}$ model that includes the possibility of band structure anisotropy as well as both isotropic and anisotropic third order Rashba splitting can explain the results. The isotropic third order contribution to the Rashba Hamiltonian is found to be negative, reducing the energy splitting at high $k$. The interplay of band structure, higher order Rashba effect and tuneable doping offers the opportunity to engineer not only the size of the spin-orbit splitting but also its direction.

Influence of constant electric field on circular photogalvanic effect in material with Rashba Hamiltonian

An appearance of a direct current perpendicularly to a constant component of an electric field in material with Rashba Hamiltonian under the influence of an elliptically polarized wave is investigated in one-subband approximation. On its physical nature this effect is close to a circular photogalvanic effect (CPGE) on intraband transitions. The effect is studied on the base of two approaches: investigations of Boltzmann kinetic equation in a constant collision frequency approximation and semiclassical Monte Carlo simulations, which immediately takes into account microscopic processes of charge carriers scattering on optical and acoustical phonons. Monte Carlo modelling allows us to determine a mean relaxation time and its dependencies on electric field strengths and on the energy of optical phonons. On the base of these estimations a possibility of using a constant relaxation time approximation is justified. It is confirmed that the main contribution to the effects of transverse rectification is made by inelastic scattering of electrons on optical phonons. A comparison of results of Monte Carlo simulations and calculations on the base of a constant collision frequency approximation is presented.

Dzyaloshinskii-Moriya–type interaction and Lifshitz invariant in Rashba 2D electron gas systems

The origin of chiral magnetic structures in ultrathin films of magnetic metals is analyzed. It is shown that the Lifshitz-type invariant term in the macroscopic thermodynamic potential can be derived from the spin-orbit Rashba Hamiltonian in two-dimensional electron gas (2DEG). The former is the prerequisite for the existence of spin cycloids, skyrmions and other chiral phenomena observed in thin films. The estimation of the period of spin cycloid gives the value of an order of 10 nm typical for structures reported in the literature.

Efficient spin-light emitting diodes based on InGaN/GaN quantum disks at room temperature: a new self-polarized paradigm.

A well-behaved spin-light emitting diode (LED) composed of InGaN/GaN multiple quantum disks (MQDs), ferromagnetic contact, and Fe3O4 nanoparticles has been designed, fabricated, and characterized. The degree of circular polarization of electroluminescence (EL) can reach up to a high value of 10.9% at room temperature in a low magnetic field of 0.35 T, which overcomes a very low degree of spin polarization in nitride semiconductors due to the weak spin-orbit interaction. Several underlying mechanisms play significant roles simultaneously in this newly designed device for the achievement of such a high performance. Most of all, the vacancy between nanodisks can be filled by half-metal nanoparticles with suitable energy band alignment, which enables selective transfer of spin polarized electrons and holes and leads to the enhanced output spin polarization of LED. Unlike previously reported mechanisms, this new process leads to a weak dependence of spin relaxation on temperature. Additionally, the internal strain in planar InGaN/GaN multiple quantum wells can be relaxed in the nanodisk formation process, which leads to the disappearance of Rashba Hamiltonian and enhances the spin relaxation time. Our approach therefore opens up a new route for the further research and development of semiconductor spintronics.

A Note on the Spectrum of a Two-particle Rashba Hamiltonian

In a series of recent papers it was shown that, when the attractive s-wave interaction is dominant, the spin-orbit coupled fermions form a bound state. Attributed to a convenient momentum representation, it became a common condition of agreement to express the bound state as a function of the center-of-mass momentum Q. In this letter we prove that the bound state of Rashba fermions does not depend on the chosen representation. That is, all the states characterized by nonzero Q fail to obey the translation symmetry.

Magnetically Generated Spin-Orbit Coupling for Ultracold Atoms

We present a new technique for producing two- and three-dimensional Rashba-type spin-orbit couplings for ultracold atoms without involving light. The method relies on a sequence of pulsed inhomogeneous magnetic fields imprinting suitable phase gradients on the atoms. For sufficiently short pulse durations, the time-averaged Hamiltonian well approximates the Rashba Hamiltonian. Higher order corrections to the energy spectrum are calculated exactly for spin-1/2 and perturbatively for higher spins. The pulse sequence does not modify the form of rotationally symmetric atom-atom interactions. Finally, we present a straightforward implementation of this pulse sequence on an atom chip.

OPTICAL CONDUCTANCE OF A TWO-DIMENSIONAL SEMICONDUCTOR IN THE PRESENCE OF RASHBA SPIN-ORBIT COUPLING AND A PERIODIC POTENTIAL

We investigate the optical conductivity of a two-dimensional semiconductor with Rashba spin-orbit coupling subject to an external sinusoidal potential. Using Fourier series, we obtain quantitative results on the band structure of this system. The periodic potential can be treated as a perturbation of the Rashba Hamiltonian, with the induced band gap at degeneracy point being linear with the potential strength. The optical conductance displays a number of interesting features, namely the presence of multiple tunable resonances that originate from a k-shift of band extrema.

The effect of spin-orbit interaction on the dynamics of ultimately short pulses in graphene systems

The effect of the spin-orbit interaction of graphene electrons placed on a Ni (111) surface on the dynamics ultimately short pulses is considered. The dispersion law of electrons in graphene is calculated on the basis of the Rashba Hamiltonian. The dynamics of an ultimately short electromagnetic pulse considering the Rashba interaction and without it is under investigation.

Possibility of entanglement transfer in a uniform electric field

By using the Rashba Hamiltonian, the evolution of entanglement of two spin-$\frac{1}{2}$ charged particles in a homogeneous electric field is investigated. It is shown that Bell states become disentangled within finite time and there exist unentangled spin states that stay unentangled during evolution. The correlations among spin-spin, momentum-momentum, and spin-momentum entanglements are discussed in detail. Moreover, a state is constructed to illustrate the fact that spin-momentum entanglement is solely a dynamical effect that can arise without any entanglement of the other degree of freedom. The results are also extended to the mixed states where Werner states are treated.

Realistic Rashba and Dresselhaus spin-orbit coupling for neutral atoms

We describe a new class of atom-laser coupling schemes which lead to spin-orbit coupled Hamiltonians for ultra-cold neutral atoms. By properly setting the optical phases, a pair of degenerate pseudospin states emerge as the lowest energy states in the spectrum, and are thus immune to collisionally induced decay. These schemes use $N$ cyclically coupled ground or metastable internal states. We specialize to two situations: a three level case giving fixed Rashba coupling, and a four-level case that adds a controllable Dresselhaus contribution. We describe an implementation of the four level scheme for $\Rb87$ and analyze the sensitivity of our approach to realistic experimental limitations and imperfections. Lastly, we argue that no laser coupling scheme can give pure Rashba or Dresselhaus coupling: akin to condensed matter systems, higher order terms spoil the symmetry of these couplings. However, for sufficiently intense laser fields the continuous rotational symmetry approximately holds, making the Rashba Hamiltonian applicable for cold atoms.

Wave packet splitting and zitterbewegung in two-dimensional semiconductor structures with spin-orbit coupling

Dynamics of electron wave packets in an asymmetric quantum well in the presence of Rashba spinorbit coupling was analytically and numerically studied. Electron Green’s functions were introduced and the evolution of 1D and 2D wave packets was studied. The effect of packet splitting caused by the presence of two branches with different chiralities in the Rashba Hamiltonian spectrum and zitterbewegung, i.e., packet center’s jitter, was studied. Spatial components of the spin density were calculated. It was shown that the component of the spin density Sy in split parts of the wave packet has opposite signs, and two other spin density components oscillate in space between scattering packets.

Current-induced spin polarization in a two-dimensional hole gas

We investigate the current-induced spin polarization in the two-dimensional hole gas (2DHG) with the structure inversion asymmetry. By using the perturbation theory, we rederive the effective $k$-cubic Rashba Hamiltonian for 2DHG and the generalized spin operators accordingly. Then based on the linear response theory, we analytically and numerically calculate the current-induced spin polarization with the disorder effect considered. We have found that, quite different from the two-dimensional electron gas, the spin polarization in 2DHG linearly depends on Fermi energy in the low-doping regime, and with increasing Fermi energy, the spin polarization may be suppressed and even changes its sign. We predict a pronounced peak of the spin polarization in 2DHG once the Fermi level is somewhere between the minimum points of two spin-split branches of the lowest light-hole subband. We discuss the possibility of measurements in experiments as regards the temperature and the width of quantum wells.

Spin Conductance of the Quantum Wire

The electron spin transport along a semiconducting quantum wire connected to spin-unpolarized electron reservoirs and the spin ltering properties of the wire are investigated. The wire is immersed in a magnetic eld that is perpendicular to the wire axis and substrate plane on which the wire is grown. The lateral conning potential is assumed to be parabolic. The spinnorbit interaction is included via Rashba Hamiltonian that in conjunction with the Zeeman Hamiltonian determines the spin conductance of the wire. Dependences of the spin current and conductance on the voltage applied over the ends of the wire as well as on the magnetic eld strength are analysed.