Spin-split Energy Bands Research Articles

Enhanced Nonlinear Response by Manipulating the Dirac Point at the (111) LaTiO_{3}/SrTiO_{3} Interface.

Tunable spin-orbit interaction (SOI) is an important feature for future spin-based devices. In the presence of a magnetic field, SOI induces an asymmetry in the energy bands, which can produce nonlinear transport effects (V∼I^{2}). Here, we focus on such effects to study the role of SOI in the (111) LaTiO_{3}/SrTiO_{3} interface. This system is a convenient platform for understanding the role of SOI since it exhibits a single-band Hall response through the entire gate-voltage range studied. We report a pronounced rise in the nonlinear longitudinal resistance at a critical in-plane field H_{cr}. This rise disappears when a small out-of-plane field component is present. We explain these results by considering the location of the Dirac point formed at the crossing of the spin-split energy bands. An in-plane magnetic field pushes this point outside of the Fermi contour, and consequently changes the symmetry of the Fermi contours and intensifies the nonlinear transport. An out-of-plane magnetic field opens a gap at the Dirac point, thereby significantly diminishing the nonlinear effects. We propose that magnetoresistance effects previously reported in interfaces with SOI could be comprehended within our suggested scenario.

Strain-modulated anomalous circular photogalvanic effect in p-type GaAs

The influence of spatial strain distribution on the anomalous circular photogalvanic effect (ACPGE) is investigated in the p-type GaAs material. By tuning the position of exerted stress, it is experimentally observed that the uniform strain related ACPGE behaves like the sine function, which resembles the non-strain situation. Whereas the gradient strain related ACPGE shows the unimodal function line shape. To explain the observations, a new theoretical model is constructed based on spin splitting of energy bands. It is demonstrated that the ACPGE could purely derive from the spin splitting effect. Besides, the combination effect of spin splitting and inverse spin Hall effect on the ACPGE is also investigated. This work reveals the importance of bands spin splitting on ACPGE, which has not been considered before.

Phase diagram of the square-lattice Hubbard model with Rashba-type antisymmetric spin-orbit coupling

We clarify the ground-state phase diagram of the half-filled square-lattice Hubbard model with Rashba spin-orbit coupling (SOC) characterized by the spin-split energy bands due to broken inversion symmetry. Although the Rashba metals and insulating magnets have been studied well, the intermediate interaction strength of the system remained elusive due to the lack of appropriate theoretical tools to unbiasedly describe the large-scale magnetic structures. We complementarily apply four different methods (sine-square deformed mean-field theory, random phase approximation, Luttinger-Tisza method, and density matrix embedding theory) and succeed in capturing the incommensurate spin-density-wave (SDW) phases with very long spatial periods which were previously overlooked. The transition to the SDW phases from the metallic phase is driven by an unprecedented instability that nests the two parts of the Fermi surface carrying opposite spins. For large SOC, the spiral, stipe, and vortex phases are obtained, when the four Dirac points exist near the Fermi level and their whole linear dispersions nest by a wavelength $\ensuremath{\pi}$, opening a band gap. These two types of transition provide Fermiology that distinguishes the antisymmetric SOC systems, generating a variety of magnetic phases that start from the relatively weak correlation regime and continue to the strongly interacting limit.

Ferri-chiral compounds with potentially switchable Dresselhaus spin splitting

Spin splitting of energy bands can be induced by relativistic spin-orbit interactions in materials without inversion symmetry. Whereas polar space group symmetries permit Rashba (R-1) spin splitting with helical spin textures in momentum space, which could be reversed upon switching a ferroelectric polarization via applied electric fields, the ordinary Dresselhaus effect (D-1A) is ac-tive only in materials exhibiting nonpolar noncentrosymmetric crystal classes with atoms occupy-ing exclusively non-polar lattice sites. Consequently, the spin-momentum locking induced by D-1A is not electric field-switchable. An alternative type of Dresselhaus symmetry, referred to as D-1B, exhibits crystal class constraints similar to D-1A (all dipoles add up to zero), but unlike D-1A, at least one polar site is occupied. We find that this behavior exists in a class of ferri-chiral crys-tals, which in principle could be reversed upon a change in chirality. Focusing on alkali metal chalcogenides, we identify NaCu5S3 in the nonentiamorphic ferri-chiral structure, which exhibits CuS3 chiral units differing in the magnitude of their Cu displacements. We then synthesize NaCu5S3 (space group P6322) and confirm its ferri-chiral structure with power x-ray diffraction. Our electronic structure calculations demonstrate it exhibits D-1B spin splitting as well as a ferri-chiral phase transition, revealing spin splitting interdependent on chirality. Our electronic struc-ture calculations show that a few percent biaxial tensile strain can reduce (or nearly quench) the switching barrier separating the monodomain ferri-chiral P6322 states. We discuss what type of external stimuli might switch the chirality so as to reverse the (non-helical) Dresselhaus D-1B spin texture, offering an alternative to the traditional reversal of the (helical) Rashba spin texture.

Giant momentum-dependent spin splitting in centrosymmetric low- Z antiferromagnets

The energy vs. crystal momentum E(k) diagram for a solid (band structure) constitutes the road map for navigating its optical, magnetic, and transport properties. By selecting crystals with specific atom types, composition and symmetries, one could design a target band structure and thus desired properties. A particularly attractive outcome would be to design energy bands that are split into spin components with a momentum-dependent splitting, as envisioned by Pekar and Rashba [Zh. Eksperim. i Teor. Fiz. 47 (1964)], enabling spintronic application. The current paper provides "design principles" for wavevector dependent spin splitting (SS) of energy bands that parallels the traditional Dresselhaus and Rashba spin-orbit coupling (SOC) - induce splitting, but originates from a fundamentally different source -- antiferromagnetism. We identify a few generic AFM prototypes with distinct SS patterns using magnetic symmetry design principles. These tools allow also the identification of specific AFM compounds with SS belonging to different prototypes. A specific compound -- centrosymmetric tetragonal MnF2 -- is used via density functional band structure calculations to quantitatively illustrate one type of AFM SS. Unlike the traditional SOC-induced effects restricted to non-centrosymmetric crystals, we show that antiferromagnetic-induced spin splitting broadens the playing field to include even centrosymmetric compounds, and gives SS comparable in magnitude to the best known ('giant') SOC effects, even without SOC, and consequently does not rely on the often-unstable high atomic number elements required for high SOC. We envision that use of the current design principles to identify an optimal antiferromagnet with spin-split energy bands would be beneficial for efficient spin-charge conversion and spin orbit torque applications without the burden of requiring compounds containing heavy elements.

The Rashba Scale: Emergence of Band Anti-crossing as a Design Principle for Materials with Large Rashba Coefficient

The spin-orbit -induced spin splitting of energy bands in low symmetry compounds (the Rashba Effect) has a long-standing relevance to spintronic applications and to the fundamental understanding of symmetry breaking in solids, yet the knowledge of what controls its magnitude in different materials is difficult to anticipate. Indeed, rare discoveries of compounds with large Rashba coefficients are invariably greeted as pleasant surprises. We advance the understanding of the "Rashba Scale" using the "inverse design" approach by formulating theoretically the relevant design principle and then identifying compounds that satisfy it. We show that the presence of energy band anti-crossing provides a causal design principle of compounds with large Rashba coefficients, leading to the identification via first-principles calculations of 34 rationally designed strong-Rashba compounds. Since topological insulators must have band anti crossing, this leads us to establish an interesting cross functionality of "Topological Rashba Insulators" (TRI) that may provide a platform for the simultaneous control of spin splitting and spin-polarization.

Interdimensional effects in a three-dimensional electron gas with a Rashba spin-orbit coupling interface

We examine the bound-state and free-state contributions to the density of states in a three-dimensional electron gas with a two-dimensional interface with Rashba spin-orbit coupling. Confinement of electrons to the interface is achieved through the inclusion of an attractive potential in the interface. Motivation for our research comes from interest in heterostructure materials that exhibit the Edelstein and inverse Edelstein effects on surfaces or interfaces due to large Rashba spin-orbit coupling. By modifying the Hamiltonian of a three-dimensional free electron gas to include an interface with Rashba spin-orbit coupling and an attractive potential, we are able to calculate the bound-state and free-state wavefunctions and corresponding density of states analytically. We find that one of the spin-split energy bands in the interface has an upper bound, resulting in an enhancement of the Edelstein and inverse Edelstein effect.

Fundamental Properties of Transition-Metals-Adsorbed Graphene.

The revealing properties of transition metal (T)-doped graphene systems are investigated with the use of the first-principles method. The detailed calculations cover the bond length, position and height of adatoms, binding energy, atom-dominated band structure, adatom-induced free carrier density as well as energy gap, spin-density distributions, spatial charge distribution, and atom-, orbital- and spin-projected density-of-states (DOS). The magnetic configurations are clearly identified from the total magnetic moments, spin-split energy bands, spin-density distributions and spin-decomposed DOS. Moreover, the single- or multi-orbital hybridizations in T-C, T-T, and C-C bonds can be accurately deduced from the careful analyses of the above-mentioned physical quantities. They are responsible for the optimal geometric structure, the unusual electronic properties, as well as the diverse magnetic properties. All the doped systems are metals except for the low-concentration Ni-doped ones with semiconducting behavior. In contrast, ferromagnetism is exhibited in various Fe/Co-concentrations but only under high Ni-concentrations. Our theoretical predictions are compared with available experimental data, and potential applications are also discussed.

Optical properties of monolayer tinene in electric fields

The absorption spectra of monolayer tinene in perpendicular electric fields are studied by the tight-binding model. There are three kinds of special structures, namely shoulders, logarithmical symmetric peaks and asymmetric peaks in the square-root form, corresponding to the optical excitations of the extreme points, saddle points and constant-energy loops. With the increasing field strength, two splitting shoulder structures, which are dominated by the parabolic bands of 5pz orbitals, come to exist because of the spin-split energy bands. The frequency of threshold shoulder declines to zero and then linearly grows. The third shoulder at 0.75~0.85 eV mainly comes from (5px, 5py) orbitals. The former and the latter orbitals, respectively, create the saddle-point symmetric peaks near the M point, while they hybridize with one another to generate the loop-related asymmetric peaks. Tinene quite differs from graphene, silicene, and germanene. The special relationship among the multi-orbital chemical bondings, spin-orbital couplings and Coulomb potentials accounts for the feature-rich optical properties.

Anisotropic in-plane spin dynamics in (110)-oriented GaAs/AlGaAs multiple quantum well

We studied spin dephasing processes in GaAs/AlGaAs multiple quantum wells (MQWs) grown on a semi-insulating (110)-oriented GaAs substrate using the time-resolved Kerr rotation (TRKR) technique. The TRKR spectra gives the electron g-factor in MQWs, as well as the spin dephasing time (SDT) for electron spins within the sample plane. The electron g-factor shows a strong two-fold anisotropy, while the in-plane SDT remains almost isotropic. The anisotropy of the electron g-factor increases monotonically with the spread of more electron wave functions into the AlGaAs barrier. The two-fold symmetry of the electron g-factor is discussed with a phenomenological model based on spin splitting of energy bands caused by spin-orbit coupling.

Superconducting instability of a non-centrosymmetric system

The Fermi gas approach to the weak-coupling superconductivity in the non-centrosymmetric systems lead to a conclusion of an approximately spin-orbit coupling independent critical temperature of the singlet states as well as the triplet states defined by the order parameter aligned with the antisymmetric spin-orbit coupling vector. We indicate that the above results follow from a simplified approximation of a density of states by a constant Fermi surface value. Such a scenario does not properly account for the spin-split quasiparticle energy spectrum and reduces the spin-orbit coupling influence on superconductivity to the bare pair-breaking effect of a lifted spin degeneracy. Applying the tight-binding model, which captures the primary features of the spin-split energy band, i.e., its enhanced width and the spin-orbit coupling induced redistribution of the spectral weights in the density of states, we calculate the critical temperature of a non-centrosymmetric superconductor. We report a general tendency of the critical temperature to be suppressed by the antisymmetric spin-orbit coupling. We indicate that, the monotonic decrease of the critical temperature may be altered by the spin-orbit coupling induced van Hove singularities which, when driven to the Fermi level, generate maxima in the phase diagram. Extending our considerations to the intermediate-coupling superconductivity we point out that the spin-orbit coupling induced change of the critical temperature depends on the structure of the electronic energy band and both – the strength and symmetry of the pair potential. Finally, we discuss the mixed singlet-triplet state superconducting instability and establish conditions concerning the symmetry of the singlet and triplet counterparts as well as the range of the spin-orbit coupling energy which make such a phase transition possible.

Synthesizing Majorana zero-energy modes in a periodically gated quantum wire

We explore a scheme for engineering a one-dimensional spinless p-wave superconductor hosting unpaired Majorana zero-energy modes, using an all-electric setup with a spin-orbit coupled quantum wire in proximity to an s-wave superconductor. The required crossing of the Fermi level by a single spin-split energy band is ensured by employing a periodically modulated Rashba interaction, which, assisted by electron-electron interactions and a uniform Dresselhaus interaction, opens a gap at two of the spin-orbit shifted Fermi points. While an implementation in a hybrid superconductor-semiconductor device requires improvements upon present-day capabilities, a variant of our scheme where spin-orbit-coupled cold fermions are effectively proximity-coupled to a BEC reservoir of Feshbach molecules may provide a ready-to-use platform.

Superconducting Instability Temperature of a Non-Centrosymmetric System

We discuss a direct effect of the energy band splitting due to the antisymmetric spin–orbit coupling on the superconducting phase transition. Employing the square lattice tight-binding model we show a significant contribution of the spin-split energy band to the pair-breaking effect in the weakand intermediate-coupling non-centrosymmetric superconductors. We establish a general tendency of the spin–orbit coupling to suppress the critical temperature of the spin singlet and triplet states. For the weak-coupling systems we report a possible development of sharp maxima of the critical temperature for the band fillings which support the spin–orbit coupling induced Fermi surface singularities of the density of states. We note that the initial suppression of the most stable triplet state becomes comparable to the suppression of other triplet states in the intermediate-coupling regime of superconductivity.

Spin- and Angle-Resolved Photoemission of Strongly Spin–Orbit Coupled Systems

In this review article, we present recent studies of peculiar Rashba spin-split energy band structures appearing at surfaces of metallic and semiconducting substances as well as surfaces of topological insulators utilizing state-of-the-art spin- and angle-resolved photoemission spectroscopy. It is shown in this article that spin- and angle-resolved spectroscopy plays very important roles in clarifying the spin-split surface and bulk band structures of Rashba-type spin-split systems and topological insulators. This article starts with instructive descriptions of the Rashba effect and topological insulators, which is followed by the history and recent development of spin- and angle-resolved photoemission spectroscopy.

Spin-Dependent Energy Bands and Spin Polarization in Two-Dimensional Spin-Orbit Lateral Superlattices

In this work, we theoretically investigate the spin-split energy bands of electrons and spin-polarized transport in two-dimensional (2D) spin-orbit lateral superlattices (SOLSLs), where the square rods with Rashba spin-orbit coupling (SOC) are distributed periodically by applying gate voltages on the semiconductor. Within the Landauer framework of ballistic transport, the energy bands, the electrical conductance, the spin polarization and the spin-dependent electronic charge distributions have been calculated. It is found that the energy minibands are formed and the energy levels are split up by the Rashba SOC. As a result, the spin-polarized conductance is obtained even in the absence of external magnetic fields and magnetic materials. Meanwhile, the spin polarization can approach high values in the SOLSLs by manipulating the strength of SOC. Furthermore, the spin-dependent electronic charge distributions have been obtained, which present a clear picture of spin-polarized conductance. Our investigations have the potential applications in spin-based quantum devices and semiconductor spintronics.

Spin-dependent scattering by a potential barrier on a nanotube

The electron spin effects on the surface of a nanotube have been considered throughthe spin–orbit interaction (SOI), arising from the electron confinement on thesurface of the nanotube. This is of the same nature as the Rashba–Bychkov SOIat a semiconductor heterojunction. We estimate the effect of disorder within apotential barrier on the transmission probability. Using a continuum model, weobtain analytic expressions for the spin-split energy bands for electrons on thesurface of nanotubes in the presence of SOI. First we calculate analytically theamplitudes of scattering from a potential barrier located around the axis of thenanotube into spin-dependent states. The effect of disorder on the scatteringprocess is included phenomenologically and induces a reduction in the transitionprobability. We analyze the relative role of SOI and disorder in the transmissionprobability which depends on the angular and linear momentum of the incomingparticle, and its spin orientation. Finally we demonstrate that in the presenceof disorder, perfect transmission may not be achieved for finite barrier heights.

Study of Surface Rashba Effect by Spin- and Angle-Resolved Photoelectron Spectroscopy

Spin-split energy band structure appears in the surface state due to a broken space inversion symmetry at the surface boundary as well as a strong spin-orbit coupling. Spin- and angle-resolved photoemission spectroscopy (spin-resolved ARPES) has been applied to the study of the spin-split energy band structures of non-magnetic solid surfaces. First of all, some explanation of the spin-splitting mechanism for free electrons, so-called Rashba effect, will be given. Next, our spin-resolved ARPES system equipped with the compact Mott-type spin polarimeter will be introduced. We will show how the surface Rashba effect is observed from the spin-resolved ARPES with the recent result for the surface states of Bi(111). Here, we have observed strong and anti-symmetric spin polarizations with respect to the center of surface Brillouin zone in the surface states of Bi(111).

Lateral-surface superlattices in systems with spin-orbit coupling: Quantum states and bloch oscillations in an electric field

The quantum states of a two-dimensional electron gas with spin-orbit coupling located in the periodic potential of a lateral-surface superlattice are studied. The spin-split energy bands and the distribution of spin projections in the Brillouin zone are constructed. Bloch oscillations accompanied by spin precession in superlattices with spin-orbit coupling located in a constant electric field are studied.

Field Dependence of Spin Lifetimes in Wurtzite Materials

We present first-principles calculations of the zero field spin splitting of energy bands in wurtzite materials. Our calculations reveal that the huge electric fields originating from strong piezoand pyroelecric character of nitrides do not increase the spin splitting of bands in nitride heterostructures. This implicates long spin lifetimes in quantum structures based on these materials and weak possibility of tuning with external electric field.

Resonant Spin Splitting in III-V Semiconductors

We present flrst-principles studies of the zero fleld spin splitting of energy bands in typical III{V semiconductors. Our calculations reveal that the strain induces linear-k spin splitting of the conduction band in the i point, which is linear in strain, and determine the magnitude of the so-called acoustic phonon constant that characterizes the magnitude of the spin splitting. In addition, we show that optical phonons lead to spin-∞ip processes and we present quantitative results for the spin-phonon deformation potentials in GaAs. Most importantly, the calculations show that the linear-k spin splitting can be resonantly enhanced when bands cross in a particular point of the Brillouin zone. This resonant enhancement of the bulk inversion asymmetry coupling constant by more than one order of magnitude was observed in both valence and conduction bands and can be steered by the application of the external stress. This allows tailoring of the spin relaxation and spin precession of conduction electrons in nanostructures to a much larger extent than was hitherto assumed.