We consider a two-dimensional electron gas with Rashba's spin-orbit interaction and two in-plane potentials superimposed along directions perpendicular to each other. The first of these potentials is assumed to be a general periodic potential while the second one is totally arbitrary. A general form for Bloch's amplitude is found and an eigen-value problem for the band structure of the system is derived. We apply the general result to the two particular cases in which either the second potential represents a harmonic in-plane confinement or it is zero. We find that for a harmonic confinement regions of the Brillouin zone with high polarizations are associated with the ones of large group velocity.
We consider the dynamics of a quantum particle held in a lattice potential, and subjected to a time-dependent spin-orbit coupling. Tilting the lattice causes the particle to perform Bloch oscillations, and by suitably changing the Rashba interaction during its motion, the spin of the particle can be gradually rotated. Even if the Rashba coupling can only be altered by a small amount, large spin-rotations can be obtained by accumulating the rotation from successive oscillations. We show how the time-dependence of the spin-orbit coupling can be chosen to maximize the rotation per cycle, and thus…
We study the Bloch spectrum and spin physics of 2D massless Dirac electrons in single layer graphene subject to a one dimensional periodic Kronig-Penney potential and Rashba spin-orbit coupling. The Klein paradox exposes novel features in the band dispersion and in graphene spintronics. In particular it is shown that: (1) The Bloch energy dispersion $\veps(p)$ has unusual structure: There are {\it two Dirac points} at Bloch momenta $\pm p \ne 0$ and a narrow band emerges between the wide valence and conduction bands. (2) The charge current and the spin density vector vanish. (3) Yet, all the n…
We demonstrate the appearance of zero-energy bound states satisfying the $\mathbb{Z}_4$ parafermionic algebra in interacting quantum wires with Rashba spin-orbit coupling and proximity-induced superconductivity. The fourfold degeneracy of these states is protected by time-reversal symmetry and fermion-parity conservation, and leads to an $8 π$ periodicity of the Josephson current due to the tunneling of fractionalized excitations with charge $e/2$. Even in the presence of perturbations, we propose that this periodicity will remain visible in driven, current-biased Shapiro step measurements on …
We theoretically study phonon-drag contribution to the thermoelectric power and hot-electron energy-loss rate in a Rashba spin-orbit coupled two-dimensional electron system (2DES) in the Bloch-Gruneisen (BG) regime. We assume that electrons interact with longitudinal acoustic phonons through deformation potential and with both longitudinal and transverse acoustic phonons through piezoelectric potential. Effect of the Rashba spin-orbit interaction on magnitude and temperature dependence of the phonon-drag thermoelectric power and hot-electron energy-loss rate are discussed. We numerically extra…
We study phonon-drag contribution to the thermoelectric power in a quasi-two-dimensional electron system confined in GaAs/AlGaAs heterostructure in presence of both Rashba spin-orbit interaction and perpendicular magnetic field at very low temperature. It is observed that the peaks in the phonon-drag thermopower split into two when the Rashba spin-orbit coupling constant is strong. This splitting is a direct consequence of the Rashba spin-orbit interaction. We show the dependence of phonon-drag thermopower on both magnetic field and temperature numerically. A power-law dependence of phonon-dra…
We investigate the spin relaxation due to the random Rashba spin-orbit coupling in symmetric GaAs (110) quantum wells from the fully microscopic kinetic spin Bloch equation approach. All relevant scatterings, such as the electron-impurity, electron--longitudinal-optical-phonon, electron--acoustic-phonon, as well as electron-electron Coulomb scatterings are explicitly included. It is shown that our calculation reproduces the experimental data by Müller {\em et al.} [Phys. Rev. Lett. {\bf 101}, 206601 (2008)] for a reasonable choice of parameter values. We also predict that the temperature depen…
Disorder scattering and spin-orbit coupling are together responsible for the diffusion and relaxation of spin-density in time-reversal invariant systems. We study spin-relaxation and diffusion in a two-dimensional electron gas with Rashba spin-orbit coupling and spin-independent disorder, focusing on the role of Rashba spin-orbit coupling in transport. Spin-orbit coupling contributes to spin relaxation, transforming the quantum interference contribution to conductivity from a negative weak localization (WL) correction to a positive weak anti-localization (WAL) correction. The importance of spi…
We investigate the properties of persistent charge current driven by magnetic flux in a quasi-periodic mesoscopic Fibonacci ring with Rashba and Dresselhaus spin-orbit interactions. Within a tight-binding framework we work out individual state currents together with net current based on second-quantized approach. A significant enhancement of current is observed in presence of spin-orbit coupling and sometimes it becomes orders of magnitude higher compared to the spin-orbit interaction free Fibonacci ring. We also establish a scaling relation of persistent current with ring size, associated wit…
We study the effects of spin-orbit interaction (SOI) on the current-induced motion of a magnetic (Bloch) domain wall in ultrathin ferromagnetic nanowires. The conspiracy of spin relaxation and SOI is shown to generate a novel strong nonequilibrium Rashba field, which is dominant even for moderate SOI. This field causes intricate spin precession and a transition from translatory to oscillatory wall dynamics with increasing SOI. We show that current pulses of different lengths can efficiently be used to control the domain wall motion.
In this work we study the effects of a longitudinal periodic potential on a parabolic quantum wire defined in a two-dimensional electron gas with Rashba spin-orbit interaction. For an infinite wire superlattice we find, by direct diagonalization, that the energy gaps are shifted away from the usual Bragg planes due to the Rashba spin-orbit interaction. Interestingly, our results show that the location of the band gaps in energy can be controlled via the strength of the Rashba spin-orbit interaction. We have also calculated the charge conductance through a periodic potential of a finite length …
A spin-qubit transformation protocol is proposed for an electron in a mesoscopic quantum ring with tunable Rashba interaction controlled by the external electric field. The dynamics of an electron driven around the ring by a series of Landau-Zenner-like transitions between a finite number of local voltage gates is determined analytically. General single-qubit transformations are demonstrated to be feasible in a dynamical basis of localized pseudo-spin states. It is also demonstrated that by the use of suitable protocols based on changes of the Rashba interaction full Bloch sphere can be covere…
We prove that curvature effects in low-dimensional nanomaterials can promote the generation of topological states of matter by considering the paradigmatic example of quantum wires with Rashba spin-orbit coupling, which are periodically corrugated at the nanometer scale. The effect of the periodic curvature generally results in the appearance of insulating phases with a corresponding novel butterfly spectrum characterized by the formation of fine measure complex regions of forbidden energies. When the Fermi energy lies in the gaps, the system displays localized end states protected by topology…
We consider periodically-driven arrays of weakly coupled wires with conduction and valence bands of Rashba type and study the resulting Floquet states. This non-equilibrium system can be tuned into non-trivial phases such as of topological insulators, Weyl semimetals, and dispersionless zero-energy edge mode regimes. In the presence of strong electron-electron interactions, we generalize these regimes to the fractional case, where elementary excitations have fractional charges $e/m$ with $m$ being an odd integer.
We study the interaction between electron and acoustic phonon in a Rashba spin-orbit coupled two dimensional electron gas using Boltzmann transport theory. Both deformation potential and piezoelectric scattering mechanisms are considered in the Bloch-Gruneisen (BG) as well as in the equipartition (EP) regimes. Effect of the Rashba spin-orbit interaction on the temperature dependence of resistivity in the BG and EP regimes has been discussed. We find effective exponent of the temperature dependence of the resistivity in the BG regime decreases due to spin-orbit coupling.
We study the Landau-Zener tunneling problem for particles bound in periodic lattice insulators. To this end, we construct the path integral based on the Bloch and Wannier functions in the presence with an external force, and the transition amplitude is calculated for the Su-Schrieffer-Heeger model. We find that the tunneling probability in bulk periodic systems becomes drastically larger than that by the Landau-Zener formula. This enhancement is prominent for small values of the external field or small hopping integral compared with the gap, and comes from the difference between the Dirac and …
We study an atomic chain in the presence of modulated charge potential and modulated Rashba spin-orbit coupling (RSOC) of equal period. We show that for commensurate periodicities $λ=4 n$ with integer $n$, the three-dimensional synthetic space obtained by sliding the two phases of the charge potential and RSOC features a topological nodal line semimetal protected by an antiunitary particle-hole symmetry. The location and shape of the nodal lines strongly depend on the relative amplitude between the charge potential and RSOC.
In spatially periodic Hermitian systems, such as electronic systems in crystals, the band structure is described by the band theory in terms of the Bloch wave functions, which reproduce energy levels for large systems with open boundaries. In this paper, we establish a generalized Bloch band theory in one-dimensional spatially periodic tight-binding models. We show how to define the Brillouin zone in non-Hermitian systems. From this Brillouin zone, one can calculate continuum bands, which reproduce the band structure in an open chain. As an example, we apply our theory to the non-Hermitian Su-…
We developed the theory of electronic properties of semiconductor quantum rings with the Rashba spin-orbit interaction irradiated by an off-resonant high-frequency electromagnetic field (dressing field). Within the Floquet theory of periodically driven quantum systems, it is demonstrated that the dressing field drastically modifies all electronic characteristics of the rings, including spin-orbit coupling, effective electron mass and optical response. Particularly, the present effect paves the way to controlling the spin polarization of electrons with light in prospective ring-shaped spintroni…
We identify a series of topological transitions occurring in electronic spin transport when manipulating spin-guiding fields controlled by the geometric shape of mesoscopic interferometers. They manifest as distinct inversions of the interference pattern in quantum conductance experiments. We establish that Rashba square loops develop weak-(anti)localization transitions (absent in other geometries as Rashba ring loops) as an in-plane Zeeman field is applied. These transitions, boosted by non-adiabatic spin scattering, prove to have a topological interpretation in terms of winding numbers chara…
Inspired by recent experiments with cold atoms in optical lattices, we consider a Stückelberg interferometer for a particle performing Bloch oscillations in a tight-binding model on the honeycomb lattice. The interferometer is made of two avoided crossings at the saddle points of the band structure (i.e. at M points of the reciprocal space). This problem is reminiscent of the double Dirac cone Stückelberg interferometer that was recently studied in the continuum limit [Phys. Rev. Lett. 112, 155302 (2014)]. Although the two problems share similarities -- such as the appearance of a geometric ph…
Two connected equiperiodic one-dimensional multi-well potentials of different well depths are studied. Floquet/Bloch energy bands for respective multi-well potential are found to be relevant for understanding level structures. Althoug energies are classically allowed in both multi-well potentials, a band gap of one multi-well potential makes this potential quantum-mechanically 'forbidden'. All energy levels are located in the union of the band regions.
Spin-dependent electron transport in a periodically stubbed quantum wire in the presence of Rashba spin-orbit interaction (SOI) is studied via the nonequilibrium Green's function method combined with the Landauer-Buttiker formalism. The coexistence of spin filtering, charge and spin switching are found in the considered system. The mechanism of these transport properties is revealed by analyzing the total charge density and spin-polarized density distributions in the stubbed quantum wire. Furthermore, periodic spin-density islands with high polarization are also found inside the stubs, owing t…
Interaction between electron and acoustic phonon in an in-plane magnetic field induced gapped quantum wire with Rashba spin-orbit interaction is studied. We calculate acoustic phonon limited resistivity ($ρ$) and phonon-drag thermopower ($S_g$) due to two well known mechanisms of electron-phonon interaction namely, deformation potential (DP) and piezoelectric (PE) scattering. In the so called Bloch-Gruneisen temperature limit both $ρ$ and $S_g$ depend on temperature ($T$) in a power law fashion i.e. $ρ$ or $S_g\sim T^{ν_T}$. For resistivity, $ν_T$ takes the value $5$ and $3$ due to DP and PE s…
We solve analytically the energy eigenvalue problem of narrow semiconductor quantum rings with a general spin-orbit term that includes as a special case the Rashba and Dresselhaus interactions acting simultaneously. The eigenstates and eigenenergies of the system are found for arbitrary values of the spin-orbit coupling constants without making use of approximations. The general eigenstates are expressed as products of a scalar Mathieu function and a spinor factor which is periodic or pseudo-periodic on the ring. Our general solution reduces to the previously found solutions for particular com…
The Bloch theorem enables reduction of the eigenvalue problem of the single-particle Hamiltonian that commutes with translational group. Based on a group theory analysis we present generalization of the Bloch theorem that incorporates all additional symmetries of a crystal. The generalized Bloch theorem constrains the form of the Hamiltonian which becomes manifestly invariant under additional symmetries. In the case of isotropic interactions the generalized Bloch theorem gives a unique Hamiltonian. This Hamiltonian coincides with the Hamiltonian in the periodic gauge. In the case of anisotropi…
A transmission phenomenon for a quantal particle scattered through a multi-well potential in one dimension is observed by means of an amplitude-phase method. The potential model consists of $N$ identical potential cells, each containing a symmetric well. Typical transmission bands contain $N-1$ possible energies of total transmission. It is found that certain band types contain $n$ energies of total transmission. A fusion phenomenon of this type of band with a typical neigboring band is also found. As the transmission gap between them collapse and disappear, a resulting fused single band is se…
We describe some applications of group- and bundle-theoretic methods in solid state physics, showing how symmetries lead to a proof of the localization of electrons in gapped crystalline solids, as e.g. insulators and semiconductors. We shortly review the Bloch-Floquet decomposition of periodic operators, and the related concepts of Bloch frames and composite Wannier functions. We show that the latter are almost-exponentially localized if and only if there exists a smooth periodic Bloch frame, and that the obstruction to the latter condition is the triviality of a Hermitian vector bundle, call…
Aiming to understand the main spin relaxation mechanism in graphene, we investigate the spin relaxation with random Rashba field induced by both adatoms and substrate, by means of the kinetic spin Bloch equation approach. The charged adatoms on one hand enhance the Rashba spin-orbit coupling locally and on the other hand serve as Coulomb potential scatterers. Both effects contribute to spin relaxation limited by the D'yakonov-Perel' mechanism. In addition, the random Rashba field also causes spin relaxation by spin-flip scattering, manifesting itself as an Elliott-Yafet--like mechanism. Both m…
We derive an effective continuum model for describing the propagation of electrons in ballistic one-dimensional curved nanostructure which are marked by a strong interplay of spin-orbital degrees of freedom due to local electronic states with $d-$orbital symmetry, atomic spin-orbit and orbital Rashba couplings. We demonstrate how a planar inhomogeneous spatial curvature of the nanochannel can generate both spin and orbital textures represented through loops on the corresponding Bloch spheres. In particular, we employ the paradigmatic case of an elliptically shaped quantum ring to investigate t…
We present a detailed analysis of the spin-flip excitations induced by a periodic time-dependent electric field in the Rashba prototype Au(111) noble metal surface. Our calculations incorporate the full spinor structure of the spin-polarized surface states and employ a Wannier-based scheme for the spin-flip matrix elements. We find that the spin-flip excitations associated with the surface states exhibit an important angular modulation which is completely absent in the standard Rashba model \cite{rashba}. Furthermore, we demonstrate that the maximum of the calculated spin-flip absorption rate …
We analyze the dynamics of the helical edge modes of a quantum spin Hall state in the presence of a spatially non-uniform Rashba spin-orbit (SO) interaction. A randomly fluctuating Rashba SO coupling is found to open a scattering channel which causes localization of the edge modes for a weakly screened electron-electron (e-e) interaction. A periodic modulation of the SO coupling, with a wave number commensurate with the Fermi momentum, makes the edge insulating already at intermediate strengths of the e-e interaction. We discuss implications for experiments on edge state transport in a HgTe qu…
Electrons in a lattice exhibit time-periodic motion, known as Bloch oscillation, when subject to an additional static electric field. Here we show that a corresponding dynamics can occur upon replacing the spatially periodic potential by a time-periodic driving: Floquet oscillations of charge carriers in a spatially homogeneous system. The time lattice of the driving gives rise to Floquet bands that take on the role of the usual Bloch bands. For two different drivings (harmonic driving and periodic kicking through pulses) of systems with linear dispersion we demonstrate the existence of such o…
This work provides a convenient and powerful means towards the engineering of Floquet bands via Bloch oscillations, by adding a tilted linear potential to periodically driven lattice systems. The added linear field not only restricts the spreading of a time-evolving wavepacket but also, depending on the ratio between the Bloch oscillation frequency and the modulation frequency of the periodic driving, dramatically modifies the band profile and topology. Specifically, we consider a driven Aubry-André-Harper model as a working example, in the presence of a linear field. Almost flat Floquet bands…
