Rashba Coupling Research Articles

Kerr nonlinearity in asymmetric disc-like quantum dot and its controllability

Nonlinear Kerr materials have the potential to be used as principal components for developing optical quantum computers. Among these materials, quantum dots have high nonlinearity and high Kerr-dispersion. This paper investigated the Kerr effect in a doped asymmetric quantum dot. The results showed that third-order nonlinear optical property such as the Kerr effect can be controlled by Rashba coupling. Experimentally, the strength of Rashba coupling can be changed and thus manipulated by applying a voltage to the electrostatic gate installed on the two-dimensional plane of quantum dots. The numerical calculations illustrated that the presence of attractive impurity and enhancement of the strength of Rashba coupling in an asymmetric quantum dot increase the Kerr nonlinearity. Furthermore, the results demonstrated that the magnitude of the Kerr effect of a symmetric doped quantum dot is larger than an asymmetric doped quantum dot.

OpenMP solver for rotating spin-1 spin–orbit- and Rabi-coupled Bose–Einstein condensates

We present OpenMP version of a Fortran program for solving the Gross–Pitaevskii equation for a harmonically trapped three-component rotating spin-1 spinor Bose–Einstein condensate (BEC) in two spatial dimensions with or without spin–orbit (SO) and Rabi couplings. The program uses either Rashba or Dresselhaus SO coupling. We use the split-step Crank–Nicolson discretization scheme for imaginary- and real-time propagation to calculate stationary states and BEC dynamics, respectively. New version program summaryProgram title: BEC-GP-SPINOR-ROT-OMP, a program package containing programs spin-SO-rot-imre2d-omp.f90, with util.f90.CPC Library link to program files:https://doi.org/10.17632/j3wr4wn946.2Licensing provisions: Apache License 2.0Programming language: OpenMP Fortran 90/95. The program is tested with the GNU, Intel, PGI, and Oracle (former Sun) compilers.Supplementary material: File Supp.pdf gives additional details about the new program version and the underlying physical system.Journal Reference of previous version: Comput. Phys. Commun. 259 (2021) 107657.Does the new version supersede the previous version?: Only partially. The program spin-SO-rot-imre2d-omp.f90 supersedes spin-SO-imre2d-omp.f90, while the one-dimensional program is not part of this package.Nature of problem: The present Open Multi-Processing (OpenMP) Fortran program solves the time-dependent nonlinear partial differential Gross–Pitaevskii (GP) equation for a trapped rotating spinor Bose–Einstein condensate (BEC) in two spatial dimensions.Solution method: We employ the split-step Crank–Nicolson scheme to discretize the time-dependent GP equation in space and time. The discretized equation is then solved by imaginary- or real-time propagation, employing adequately small space and time steps, to yield the solution of stationary and non-stationary problems, respectively.Reason for new version: The BEC is a special form of matter called superfluid. A hallmark of superfluidity is the formation of quantized vortices in a rotating BEC. The present program can be used to study the generation of quantized vortices in a rotating spin-1 trapped BEC and hence should be of general interest to researchers from various fields.Summary of revisions: Previously we published Fortran [1] and C [2] programs for solving the mean-field GP equation for a BEC, which are now enjoying widespread use. Later we extended these programs to the more complex scenario of dipolar BECs [3], spin-1 spinor BECs [4], and of rotating BECs [5]. The OpenMP [6, 7] and CUDA/MPI [8, 9, 10] versions of these programs, designed to make these faster and more efficient in multi-core computers, are also available. In this paper we present Fortran 90/95 program for solving the GP equation of a two-dimensional (2D) rotating spin-1 spinor BEC with Rashba [11] and Dresselhaus [12] spin–orbit (SO) coupling and Rabi coupling, involving a modification over the same for a spin-1 spinor BEC [4]. A new input parameter OMEG, which represents the angular velocity of rotation Ω of the spin-1 spinor BEC, has been introduced in the program, following Ref. [5]. Besides this new parameter, the execution of the present program follows the same procedure as the 2D program of Ref. [4]. All other input parameters in the two programs are identical and the reader is advised to consult that reference for further details. For some values of input parameters the quantized vortices of a rotating BEC could be arranged in the form of a lattice with a certain spatial symmetry, e.g., triangular or square lattice [5]. In our numerical study, we established recently such a symmetric lattice structure for a Rashba SO-coupled rotating spin-1 BEC in the simplest case, without the Rabi coupling [13]. A Dresselhaus SO-coupled rotating spin-1 BEC should also lead to identical structure, provided the sign of the angular velocity of rotation is changed. For the sake of completeness, in the supplementary material related to this article that can be found online at URL we provide the corresponding GP equations for a rotating spin-1 BEC with some instructive numerical examples. The program package BEC-GP-SPINOR-ROT-OMP contains the programs spin-SO-rot-imre2d-omp.f90 and util.f90 in the directory src, as well as the files makefile and README.md. The makefile allows automated compilation of the program using different supported compilers (GNU, Intel, PGI, Oracle) by a simple make command, as in Ref. [4]. The file README.md contains instructions on how to compile and run the programs. The directory output contains examples of matching outputs of imaginary- and real-time propagation programs in sub-directories with a generic name rotxgamyferro or rotxgamyantiferro, where x denotes the value of the angular velocity of rotation Ω and y denotes the strength of the SO coupling γ for ferromagnetic (c0=482,c2=15) and antiferromagnetic (c0=669,c2=−3.1) cases. The results in imaginary-time sub-directories rot.3gam.5ferro and rot.3gam.5antiferro are calculated using the respective converged imaginary-time wave functions with zero angular velocity. The real-time sub-directories rot.3gam.5ferro and rot.3gam.5polar contain real-time results calculated using the respective converged imaginary-time wave functions as inputs. These sub-directories also contain gnuplot programs fig*.gnu which can be used to generate fig*.eps figure files of component densities.

Spin transport in polarization induced two-dimensional electron gas channel in c-GaN nano-wedges

A two-dimensional electron gas (2DEG), which has recently been shown to develop in the central vertical plane of a wedge-shaped c-oriented GaN nanowall due to spontaneous polarization effect, offers a unique scenario, where the symmetry between the conduction and valence band is preserved over the entire confining potential. This results in the suppression of Rashba coupling even when the shape of the wedge is not symmetric. Here, for such a 2DEG channel, relaxation time for different spin projections is calculated as a function of donor concentration and gate bias. Our study reveals a strong dependence of the relaxation rate on the spin-orientation and density of carriers in the channel. Most interestingly, relaxation of spin oriented along the direction of confinement has been found to be completely switched off. Upon applying a suitable bias at the gate, the process can be switched on again. Exploiting this fascinating effect, an electrically driven spin-transistor has been proposed.

Atom-dimer and dimer-dimer scatterings in a spin-orbit-coupled Fermi gas

Using the diagrammatic approach, here we study how spin-orbit coupling (SOC) affects the fermion-dimer and dimer-dimer scattering lengths in the Born approximation, and benchmark their accuracy with the higher-order approximations. We consider both isotropic and Rashba couplings in three dimensions, and show that the Born approximation gives accurate results in the $1/(m \alpha a_s) \ll -1$ limit, where $m$ is the mass of the fermions, $\alpha$ is the strength of the SOC, and $a_s$ is the $s$-wave scattering length between fermions. This is because the higher-loop contributions form a perturbative series in the $1/(m \alpha a_s) < 0$ region that is controlled by the smallness of the residue $Z$ of the dimer propagator. In sharp contrast, since $Z$ grows with the square-root of the binding energy of the dimer in the $1/(m \alpha a_s) > 0$ region, all of the higher-loop contributions are of similar order.

Graphene on two-dimensional hexagonal BN, AlN, and GaN: Electronic, spin-orbit, and spin relaxation properties

We investigate the electronic structure of graphene on a series of 2D hexagonal nitride insulators hXN, X = B, Al, and Ga, with DFT calculations. A symmetry-based model Hamiltonian is employed to extract orbital parameters and spin-orbit coupling (SOC) from the low-energy Dirac bands of proximitized graphene. While commensurate hBN induces a staggered potential of about 10 meV into the Dirac bands, less lattice-matched hAlN and hGaN disrupt the Dirac point much less, giving a staggered gap below 100 $\mu$eV. Proximitized intrinsic SOC surprisingly does not increase much above the pristine graphene value of 12 $\mu$eV; it stays in the window of (1-16) $\mu$eV, depending strongly on stacking. However, Rashba SOC increases sharply when increasing the atomic number of the boron group, with calculated maximal values of 8, 15, and 65 $\mu$eV for B, Al, and Ga-based nitrides, respectively. The individual Rashba couplings also depend strongly on stacking, vanishing in symmetrically-sandwiched structures, and can be tuned by a transverse electric field. The extracted spin-orbit parameters were used as input for spin transport simulations based on Chebyshev expansion of the time-evolution of the spin expectation values, yielding interesting predictions for the electron spin relaxation. Spin lifetime magnitudes and anisotropies depend strongly on the specific (hXN)/graphene/hXN system, and they can be efficiently tuned by an applied external electric field as well as the carrier density in the graphene layer. A particularly interesting case for experiments is graphene/hGaN, in which the giant Rashba coupling is predicted to induce spin lifetimes of 1-10 ns, short enough to dominate over other mechanisms, and lead to the same spin relaxation anisotropy as observed in conventional semiconductor heterostructures: 50\%, meaning that out-of-plane spins relax twice as fast as in-plane spins.

Magnetic impurities along the edge of a quantum spin Hall insulator: Realizing a one-dimensional AIII insulator

In this paper we construct a one-dimensional insulator with an approximate chiral symmetry belonging to the AIII class and discuss its properties. The construction principle is the intentional pollution of the edge of a two-dimensional quantum spin Hall insulator with magnetic impurities. The resulting bound states hybridize and disperse along the edge. We discuss under which circumstances this chain possesses zero-dimensional boundary modes on the level of an effective low-energy theory. The main appeal of our construction is the independence on details of the impurity lattice: the zero modes are stable against disorder and random lattice configurations. We also show that in the presence of Rashba coupling, which changes the symmetry class to A, one can still expect localized half-integer boundary excess charges protected by mirror symmetry although there is no nontrivial topological index. All of the results are confirmed numerically in a microscopic model.

Rashba coupling and spin switching through surface states of Dirac semimetals

We study the effect of the Rashba spin–orbit coupling on the Fermi arcs of topological Dirac semimetals. The Rashba coupling is induced by breaking the inversion symmetry at the surface. Remarkably, this coupling could be enhanced by the interaction with the substrate and controlled by an external electric field. We study analytically and numerically the rotation of the spin of the surface states as a function of the electron’s momentum and the coupling strength. Furthermore, a detailed analysis of the spin-dependent two-terminal conductance is presented in the clean limit and with the addition of a random distribution of impurities. Depending on the magnitude of the quadratic terms in the Hamiltonian, the spin-flip conductance may become dominant, thus showing the potential of the system for spintronic applications, since the effect is robust even in the presence of disorder.

Multiring, stripe, and superlattice solitons in a spin-orbit-coupled spin-1 condensate

We demonstrate exotic stable quasi-two-dimensional solitons in a Rashba or a Dresselhaus spin-orbit (SO) coupled hyperfine spin-1 ($F=1$) trap-less antiferromagnetic Bose-Einstein condensate using the mean-field Gross-Pitaevskii equation. For weak SO coupling, the solitons are of the $(-1,0,+1)$ or $(+1,0,-1)$ type with intrinsic vorticity, for Rashba or Dresselhaus SO coupling, where the numbers in the parentheses denote angular momentum in spin components $F_z= +1,0,-1$, respectively. For intermediate SO coupling, the solitons have multi-ring structure maintaining the above-mentioned vortices in respective components. For larger SO coupling, superlattice solitons with a square-lattice structure in total density are found in addition to stripe solitons with stripe pattern in component densities with no periodic modulation in total density.

The spin-filtering properties in two coupled Rashba quantum rings

The spin-dependent electron transport in two coupled quantum rings with Rashba spin-orbit interaction and magnetic flux was studied by using quantum graph approach. We show the dependence of spin-polarization on system parameters such as the Rashba coupling constant, the radius of the rings, the angles between the leads and the attachment point of the rings. The spin-polarization can be controlled and changed from -1 to +1 by using a magnetic flux. Also it was shown that this model is a limiting case of double Rashba quantum ring when the length of the middle lead between rings vanishes.

The spin-filtering properties in two coupled Rashba quantum rings

The spin-dependent electron transport in two coupled quantum rings with Rashba spin-orbit interaction and magnetic flux was studied by using quantum waveguide theory. We show the dependence of spin-polarization on system parameters such as the Rashba coupling constant, the radius of the rings, the angles between the leads and the attachment point of the rings. The spin-polarization can be controlled and changed from -1 to +1 by using a magnetic flux. Also it was shown that this model is a limiting case of double Rashba quantum ring when the length of the middle lead between rings vanishes. The same study for spin-filtering properties in two coupled quantum rings with Dresselhaus spin-orbit interaction was also obtained and the results were compared.

Energy level splitting of a 2D hydrogen atom with Rashba coupling in non-commutative space

We explore the non-commutative (NC) effects on the energy spectrum of a two-dimensional hydrogen atom. We consider a confined particle in a central potential and study the modified energy states of the hydrogen atom in both coordinates and momenta of non-commutativity spaces. By considering the Rashba interaction, we observe that the degeneracy of states can also be removed due to the spin of the particle in the presence of NC space. We obtain the upper bounds for both coordinates and momenta versions of NC parameters by the splitting of the energy levels in the hydrogen atom with Rashba coupling. Finally, we find a connection between the NC parameters and Lorentz violation parameters with the Rashba interaction.

Backscattering off a driven Rashba impurity at the helical edge

The spin degree of freedom is crucial for both understanding and exploiting the particular properties of the edges of two-dimensional topological insulators. In the absence of superconductivity and magnetism, Rashba coupling is the most relevant single particle perturbation in this system. Since Rashba coupling does not break time reversal symmetry, its influence on transport properties is only visible if processes that do not conserve the single particle energy are included. Paradigmatic examples of such processes are electron-electron interactions and time dependent external drivings. We analyze the effects of a periodically driven Rashba impurity at the helical edge, in the presence of electron-electron interactions. Interactions are treated by means of bosonization and the backscattering current is computed perturbatively up to second order in the impurity strength. We show that the backscattering current is non-monotonic in the driving frequency. This property is a fingerprint of the Rashba impurity, being absent in the case of a magnetic impurity in the helical liquid. Moreover, the non-monotonic behaviour allows us to directly link the backscattering current to the Luttinger parameter $K$, encoding the strength of electron-electron interactions.

Landau levels in spin-orbit coupling proximitized graphene: Bulk states

We study the magnetic-field dependence of Landau levels in graphene proximitized by large spin-orbit coupling materials, such as transition-metal dichalcogenides or topological insulators. In addition to the Rashba coupling, two types of intrinsic spin-orbit interactions, uniform (Kane-Mele type) and staggered (valley Zeeman type), are included, to resolve their interplay with magnetic orbital effects. Employing a continuum model approach, we derive analytic expressions for low-energy Landau levels, which can be used to extract local orbital and spin-orbit coupling parameters from scanning probe spectroscopy experiments. We compare different parameter regimes to identify fingerprints of relative and absolute magnitudes of intrinsic spin-orbit coupling in the spectra. The inverted band structure of graphene proximitized by WSe$_2$ leads to an interesting crossing of Landau states across the bulk gap at a crossover field, providing insights into the size of Rashba spin-orbit coupling. Landau level spectroscopy can help to resolve the type and signs of the intrinsic spin-orbit coupling by analyzing the symmetry in energy and number of crossings in the Landau fan chart. Finally, our results suggest that the strong response to the magnetic field of Dirac electrons in proximitized graphene can be associated with extremely large self-rotating magnetic moments.

Lorentz violation induced by Rashba coupling via non-commutative geometry

In this paper we consider a simple non-relativistic quantum system for a particle confined inside a pseudo-harmonic oscillator potential in the non-commutative space. We study the influence of non-commutative background on the energy spectrum of the particle by considering the Rashba spin-orbit interaction. We show that the Rashba interaction can generate the Lorentz violation effect in the non-commutative background, which is independent of potential. Finally, we find a compatible bound on the Lorentz violation parameter of electrons as an order of in the non-relativistic system.

Effect of Rashba Impurities on Surface State of a Topological Kondo Insulator

In this communication, we report surface state, with Rashba impurities, of a generic topological Kondo insulator (TKI) system by performing a mean-field theoretic (MFT) calculation within the framework of slave-boson protocol. The surface metallicity together with bulk insulation is found to require very strong f-electron localization. The possibility of intra-band as well as inter-band unconventional plasmons exists for the surface state spectrum. The paramountcy of the bulk metallicity, and, in the presence of the Rashba impurities, the TKI surface comprising of ‘helical liquids’ are the important outcomes of the present communication. The access to the gapless Dirac spectrum leads to spin-plasmons with the usual wave vector dependence q1/2. The Rashba coupling does not impair the Kondo screening and does not affect the quantum critical point (QCP) for the bulk.

Narrow quantum rings with general Rashba and Dresselhaus spin-orbit interactions

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 combinations of the Rashba and Dresselhaus couplings, like the well-studied cases of Rashba-only and of equal coupling constants.

Controlling spin without magnetic fields: The Bloch-Rashba rotator

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 how this method can be used to produce a precise and controllable spin-rotator, the Bloch-Rashba rotator, without requiring an applied magnetic field.

Improved effective equation for the Rashba spin-orbit coupling in semiconductor nanowires

Semiconductor Rashba nanowires are quasi-one dimensional systems that have large spin-orbit (SO) coupling arising from a broken inversion symmetry due to an external electric field. There exist parametrized multiband models that can describe accurately this effect. However, simplified single band models are highly desirable to study geometries of recent experimental interest, since they may allow to incorporate the effects of the low dimensionality and the nanowire electrostatic environment at a reduced computational cost. Commonly used conduction band approximations, valid for bulk materials, greatly underestimate the SO coupling in Zinc-blende crystal structures and overestimate it for Wurtzite ones when applied to finite cross-section wires, where confinement effects turn out to play an important role. We demonstrate here that an effective equation for the linear Rashba SO coupling of the semiconductor conduction band can reproduce the behavior of more sophisticated eight-band k$\cdot$p model calculations. This is achieved by adjusting a single effective parameter that depends on the nanowire crystal structure and its chemical composition. We further compare our results to the Rashba coupling extracted from magnetoconductance measurements in several experiments on InAs and InSb nanowires, finding excellent agreement. This approach may be relevant in systems where Rashba coupling is known to play a major role, such as in spintronic devices or Majorana nanowires.

Spin-current and pseudo-spin density response functions in graphene

Abstract Spin-current and pseudo-spin response to the electric and magnetic fields have been investigated within the Kubo approach. It has been realized that this problem can be regarded as the spin, pseudo-spin correlations and self-correlations. Calculations have been performed within the Dirac cone approximation. Meanwhile, the effect of gate induced Rashba coupling has been considered as a spin-dependent external control parameter where some experimental reports supports that spin–charge correlation can be controlled by the Rashba interaction Ghiasi et al. (2019). Calculations have been performed in the framework of the linear response regime in which the electric and magnetic perturbations are weak. Results of the present study show that the extreme frequencies of response functions could be considered as structural characteristic properties of the sample which are independent of motive and response quantities. Meanwhile, it has been shown that the response functions can effectively be controlled by the Rashba coupling.

Rashba-controlled two-electron spin-charge qubits as building blocks of a quantum computer

The spin-sensitive charge oscillation, controlled by an external magnetic field, was recently proposed as a mechanism of transformations of qubits, defined as two-electron spin-charge Wannier molecules in a square quantum dot.1 The paper expands this idea by including the effects of Rashba-type spin-orbit coupling. The problem is studied theoretically by mapping the system to an analytic effective Hamiltonian for 8 low-energy states, comprising singlet and triplet on each dot diagonal. The validity of mapping is confirmed by comparing the energy and spin of full and mapped system, and also by the reproduction of charge-oscillation dynamics in the presence of magnetic flux. The newly introduced Rashba coupling significantly enriches the system dynamics, affecting the magnitude of charge oscillations and allowing the controlled transitions between singlet and triplet states due to the spin rotations, induced by spin-orbit coupling. The results indicate the possibility for use of the studied system for quantum information processing, while possible extensions of the system to serve as a qubit in a universal quantum computer, fulfilling all five Di Vincenzo criteria, is also discussed.