Effect Of Spin-orbit Interaction Research Articles

Transformations of the transverse Poynting vector distribution upon diffraction of a circularly polarized paraxial beam.

Usually, the structure of paraxial light beams is characterized by the intensity associated with distribution of the longitudinal energy flow density (Poynting momentum) across the transverse plane. In this work, special attention is paid to the distribution of internal energy flows described by the transverse Poynting momentum (TPM) components. This approach discloses additional polarization-dependent features of the vector beam transformations; in application to the edge diffraction of a circularly polarized (CP) Gaussian beam, it reveals the helicity-dependent asymmetry of the diffracted-field TPM profile characterized by the shifts of the TPM singularity, maximum, etc. These phenomena are confirmed experimentally and interpreted in terms of the spin-orbit interaction (SOI) and spin Hall effect of light. In contrast to the known SOI manifestations in the CP beams' diffraction originating from the small longitudinal component of a paraxial field, the new TPM-related effects stem from the transverse field components and are thus much higher in magnitude.

Combined effect of rashba spin-orbit interaction, hydrostatic pressure and temperature on energy dispersion based ballistic conductance of InAs tunnel-coupled (double) quantum wire under exterior magnetic and electric field

In this work the change in energy dispersion curve and ballistic conductance for InAs tunnel-coupled double quantum wire (DQWR) under the influence of the external magnetic field, electric field, hydrostatic pressure, temperature, and Rashba spin-orbit interaction (SOI) are studied theoretically in detail. A constant magnetic field transverse to the fundamental plane is applied to the DQWR. The Landuer-Büttiker formalism is used to determine the transport characteristics, and the energy eigenvectors and eigenvalues are derived within the parameters of the diagonalization approach. The numerical results indicate that the energy spectra of the system are influenced by external factors such as magnetic field, electric field, temperature, hydrostatic pressure, and Rashba SOI, resulting in variations in lateral/vertical and downward/upward shifts. These factors also cause oscillatory patterns in ballistic conductance due to the oddity of energy subbands. These results have significant implications for the advancement of double-quantum wire-based devices.

Spin-orbit interaction effects on electronic, magnetic, and optical properties of [formula omitted]- center in a quantum dot with Gaussian confinement

In this paper, we study the binding energy, transition energy, and oscillator strength of a D0 impurity positioned at the center of a two-dimensional quantum dot. The QD is subject to a Gaussian confining potential, magnetic field, Rashba, and Dresselhaus spin-orbit interactions (SOI). The ground state and first exited state energies, and corresponding binding energies are calculated. Using the variational method with simple wave functions, transition energy, magnetic moment, and susceptibilities are obtained as a function of QD parameters, magnetic field, and SOI coupling strengths. The energies and binding energies increase with Dresselhaus SOI strength but decrease with Rashba SOI strength in a magnetic field. The magnetic moment and susceptibility of both states of a (D0) impurity show diamagnetic behaviour with both SOI strengths. Finally, we studied oscillator strength and compared the available literature, which did not consider all these effects.

Effect of intrinsic & Rashba spin-orbit interactions (SOI) in case of bilayer graphene

In this study, we investigated how various SOI affect the properties of bilayer graphene’s energy band structure. We have considered intralayer interactions in this work. We focused on the system without biasing. We found that the intrinsic spin-orbit interaction (ISOI) can produce an energy band gap in bilayer graphene. On the other hand, in the case of an intralayer Rashba spin-orbit interaction (RSOI) different energy bands exist. The results shown depicts how the behaviour of the energy bands remains the same when we are increasing the number of atoms (N) in a unit cell of bilayer graphene.

Effective dynamics for a spin-1/2 particle constrained to a curved layer with inhomogeneous thickness

We derive an effective Hamiltonian for a spin-1/2 particle confined within a curved thin layer with non-uniform thickness using the confining potential approach. Our analysis reveals the presence of a pseudo-magnetic field and effective spin–orbit interaction (SOI) arising from the curvature, as well as an effective scalar potential resulting from variations in thickness. Importantly, we demonstrate that the physical effect of additional SOI from thickness fluctuations vanishes in low-dimensional systems, thus guaranteeing the robustness of spin interference measurements to thickness imperfection. Furthermore, we establish the applicability of the effective Hamiltonian in both symmetric and asymmetric confinement scenarios, which is crucial for its utilization in one-side etching systems.

Quantum Spin Hall Effect in Two-Monolayer-Thick InN/InGaN Coupled Multiple Quantum Wells.

In this study, we present a theoretical study of the quantum spin Hall effect in InN/InGaN coupled multiple quantum wells with the individual well widths equal to two atomic monolayers. We consider triple and quadruple quantum wells in which the In content in the interwell barriers is greater than or equal to the In content in the external barriers. To calculate the electronic subbands in these nanostructures, we use the eight-band k∙p Hamiltonian, assuming that the effective spin-orbit interaction in InN is negative, which represents the worst-case scenario for achieving a two-dimensional topological insulator. For triple quantum wells, we find that when the In contents of the external and interwell barriers are the same and the widths of the internal barriers are equal to two monolayers, a topological insulator with a bulk energy gap of 0.25 meV can appear. Increasing the In content in the interwell barriers leads to a significant increase in the bulk energy gap of the topological insulator, reaching about 0.8 meV. In these structures, the topological insulator can be achieved when the In content in the external barriers is about 0.64, causing relatively low strain in quantum wells and making the epitaxial growth of these structures within the range of current technology. Using the effective 2D Hamiltonian, we study the edge states in strip structures containing topological triple quantum wells. We demonstrate that the opening of the gap in the spectrum of the edge states caused by decreasing the width of the strip has an oscillatory character regardless of whether the pseudospin-mixing elements of the effective Hamiltonian are omitted or taken into account. The strength of the finite size effect in these structures is several times smaller than that in HgTe/HgCdTe and InAs/GaSb/AlSb topological insulators. Therefore, its influence on the quantum spin Hall effect is negligible in strips with a width larger than 150 nm, unless the temperature at which electron transport is measured is less than 1 mK. In the case of quadruple quantum wells, we find the topological insulator phase only when the In content in the interwell barriers is larger than in the external barriers. We show that in these structures, a topological insulator with a bulk energy gap of 0.038 meV can be achieved when the In content in the external barriers is about 0.75. Since this value of the bulk energy gap is very small, quadruple quantum wells are less useful for realizing a measurable quantum spin Hall system, but they are still attractive for achieving a topological phase transition and a nonlocal topological semimetal phase.

Vibronic order and emergent magnetism in cubic d1 double perovskites

The synergistic interplay of different interactions in materials leads to the emergence of novel quantum phenomena. Spin-orbit and vibronic couplings usually counteract each other; however, in cubic ${d}^{1}$ double perovskites they coexist and give rise to spin-orbit-lattice entanglement with unquenched dynamic Jahn-Teller effect on the metal sites. The correlation of these entangled states induced by intersite interactions has not been assessed so far. Here, we investigate the joint cooperative effect of spin-orbit and vibronic interactions on the formation of the ordered phases in ${d}^{1}$ double perovskites. We found that the magnetically ordered states in these systems coexist with a dynamic vibronic order characterized by the ordering of vibronic quadrupole moments on sites. This treatment allows for the rationalization of a number of unexplained features of experimentally investigated phases.

Field-induced effects in the spin liquid candidate PbCuTe2O6

${\mathrm{PbCuTe}}_{2}{\mathrm{O}}_{6}$ is considered to be one of the rare candidate materials for a three-dimensional quantum spin liquid (QSL). This assessment was based on the results of various magnetic experiments, performed mainly on polycrystalline material. More recent measurements on single crystals revealed an even more exotic behavior, yielding ferroelectric order below ${T}_{\text{FE}}\ensuremath{\approx}1\phantom{\rule{0.28em}{0ex}}\text{K}$, accompanied by distinct lattice distortions, and a somewhat modified magnetic response which is still consistent with a QSL. Here we report on low-temperature measurements of various thermodynamic, magnetic, and dielectric properties of single-crystalline ${\mathrm{PbCuTe}}_{2}{\mathrm{O}}_{6}$ in magnetic fields $B\ensuremath{\le}14.5\phantom{\rule{0.28em}{0ex}}\text{T}$. The combination of these various probes allows us to construct a detailed $B\text{\ensuremath{-}}T$ phase diagram including a ferroelectric phase for $B\ensuremath{\le}8$ T and a $B$-induced magnetic phase at $B\ensuremath{\ge}11$ T. These phases are preceded by or coincide with a structural transition from a cubic high-temperature phase into a distorted noncubic low-temperature state. The phase diagram discloses a ferroelectric quantum critical point at ${B}_{c1}=7.9\phantom{\rule{0.28em}{0ex}}\text{T}$, where the second-order phase transition line associated with ferroelectric order is suppressed to zero. In addition, a magnetic quantum phase transition is revealed at ${B}_{c2}=11\phantom{\rule{0.28em}{0ex}}\text{T}$. The corresponding phase transition to a field-induced magnetic order at $B>{B}_{c2}$ is likely to be of first order. Field-induced lattice distortions, observed in the state at $T>1$ K and which are assigned to the effect of spin-orbit interaction of the ${\mathrm{Cu}}^{2+}$ ions, are considered as the key mechanism by which the magnetic field couples to the dielectric degrees of freedom in this material.

Symmetry breaking and superfluid currents in a split-ring spinor polariton condensate

Bosonic condensates of spinless noninteracting particles confined on a ring cannot propagate circular periodic currents once rotation symmetry of the system is broken. However, a persistent current may appear due to interparticle interactions exceeding some critical strength. In this up-critical regime breaking of the symmetry between the clockwise and anticlockwise rotations takes place. We consider this symmetry-breaking scenario in the case of a spinor condensate of exciton polaritons trapped on a ring split by a potential barrier. Due to the intrinsic symmetry of the effective spin-orbit interaction, which stems from the linear splitting between transverse-electric and transverse-magnetic microcavity modes, the potential barrier blocks the circulating current and imposes linear polarization patterns. On the other hand, circularly polarized polaritons form circular currents propagating in opposite directions with equal absolute values of angular momentum. In the presence of interparticle interactions, the symmetry of clockwise and anticlockwise currents can be broken spontaneously. We describe several symmetry-breaking scenarios, which imply either restoration of the global condensate rotation or the onset of the circular polarization in the symmetry-broken state.

Spin-orbit interaction effect on a hydrogenic [formula omitted] centre in a three-dimensional asymmetric Gaussian GaAs quantum dot in a magnetic field

The binding energy of a hydrogenic neutral D0 complex situated in a three-dimensional asymmetric Gaussian GaAs quantum dot is studied incorporating the Rashba and Dresselhaus spin-orbit interactions and the effect of an external magnetic field by means of a variational method and its variation with respect to the quantum dot size, strength of the magnetic field, donor position and spin-orbit coupling strengths is calculated. The behavior of the magnetic susceptibility of the system is also investigated with respect to the magnetic field for different values of the quantum dot parameters.

Protected spin-orbit induced absorption divergence in distorted Landau levels

The effect of spin-orbit (and Darwin) interaction on a 2D electron gas subject to a radial symmetric, inhomogeneous $1/r$-magnetic field is discussed analytically in a perturbative and non-perturbative manner. For this purpose, we investigate the radial Hall conductivity that emerges from an additional homogeneous electric field perturbation perpendicular to the 2D electron gas, which solely interacts via spin-orbit coupling. Numerical calculations of the absorptive spin-orbit spectra show for an ideal InSb electron gas a behaviour that is dominated by the localized (atomic) part of the distorted Landau levels. In contrast, however, we also find analytically that a (non-local) divergent static response emerges for Fermi energies close to the ionization energy in the thermodynamic limit. The divergent linear response implies that the external electric field is entirely absorbed outside the 2D electron gas by induced radial spin-orbit currents, as it would be the case inside a perfect conductor. This spin-orbit induced polarization mechanism depends on the effective $g^*$-factor of the material for which it shows a critical behaviour at $g^*_c=2$, where it abruptly switches direction. The diverging absorption relies on the presence of degenerate energies with allowed selection rules that are imposed by the radial symmetry of our inhomogeneous setup. We show analytically the presence of a discrete Rydberg-like band structure that obeys these symmetry properties. In a last step, we investigate the robustness of the spectra by solving analytically the Dirac equation expanded up to order $1/(mc)^2$. We find that the distorted Landau-levels, and thus the divergent spin-orbit polarization, remain protected with respect to slow changes of the applied $1/r$-magnetic field.

Effect of spin-orbit coupling on the zero-point renormalization of the electronic band gap in cubic materials: First-principles calculations and generalized Fröhlich model

The electronic structure of semiconductors and insulators is affected by ionic motion through electron-phonon interaction, yielding temperature-dependent band gap energies and zero-point renormalization (ZPR) at absolute zero temperature. For polar materials, the most significant contribution to the band gap ZPR can be understood in terms of the Fr\"ohlich model, which focuses on the nonadiabatic interaction between an electron and the macroscopic electrical polarization created by a long-wavelength optical longitudinal phonon mode. On the other hand, spin-orbit interaction (SOC) modifies the bare electronic structure, which will, in turn, affect the electron-phonon interaction and the ZPR. We present a comparative investigation of the effect of SOC on the band gap ZPR of twenty semiconductors and insulators with cubic symmetry using first-principles calculations. We observe a SOC-induced decrease of the ZPR, up to 30%, driven by the valence band edge, which almost entirely originates from the modification of the bare electronic eigenenergies and the decrease of the hole effective masses near the $\mathrm{\ensuremath{\Gamma}}$ point. We also incorporate SOC into a generalized Fr\"ohlich model, addressing the Dresselhaus splitting which occurs in noncentrosymmetric materials, and confirm that the predominance of nonadiabatic effects on the band gap ZPR of polar materials is unchanged when including SOC. Our generalized Fr\"ohlich model with SOC provides a reliable estimate of the SOC-induced decrease of the polaron formation energy obtained from first principles and brings to light some fundamental subtleties in the numerical evaluation of the effective masses with SOC for noncentrosymmetric materials. We finally warn about a possible breakdown of the parabolic approximation, one of the most fundamental assumptions of the Fr\"ohlich model, within the physically relevant energy range of the Fr\"ohlich interaction for materials with high phonon frequencies treated with SOC.

Proximity effect and inverse proximity effect in a topological-insulator/iron-based-superconductor heterostructure

We theoretically study the proximity effect and the inverse proximity effect in a topological insulator/iron-based superconductor heterostructure based on the microscopic model. The superconducting order parameter is self-consistently calculated. Its magnitude decreases when the coupling of these two systems increases. The induced pairing order parameter exhibits negative and positive values, while the negative pairing near the $\Gamma=(0,0)$ point is dominant. This parameter has twofold symmetry and includes an $s$-wave component and a $d$-wave component. The magnitude of the induced pairing order parameter has a maximal value at the coupling strength $t_p=0.3\approx 0.06$ eV. The spectral function and the local density of states are calculated and may be used to probe the proximity effect. We also discuss the feedback of the topological insulator to the iron-based superconductor layer. The normal-state Fermi surface is distorted by the coupling, and additional Fermi pockets are induced. An effective spin-orbit interaction term is induced. In the superconducting state, the previous fourfold symmetry of the order parameter is broken, and a $d$-wave component pairing term is also induced. Our main results can be well understood by analyzing the Fermi surfaces of the original systems.

Spin-controlled photonics via temporal anisotropy

Abstract Temporal metamaterials, based on time-varying constitutive properties, offer new exciting possibilities for advanced field manipulations. In this study, we explore the capabilities of anisotropic temporal slabs, which rely on abrupt changes in time from isotropic to anisotropic response (and vice versa). Our findings show that these platforms can effectively manipulate the wave-spin dimension, allowing for a range of intriguing spin-controlled photonic operations. We demonstrate these capabilities through examples of spin-dependent analog computing and spin–orbit interaction effects for vortex generation. These results provide new insights into the field of temporal metamaterials, and suggest potential applications in communications, optical processing and quantum technologies.

On-demand electrical control of spin qubits

Once called a 'classically non-describable two-valuedness' by Pauli, the electron spin forms a qubit that is naturally robust to electric fluctuations. Paradoxically, a common control strategy is the integration of micromagnets to enhance the coupling between spins and electric fields, which, in turn, hampers noise immunity and adds architectural complexity. Here we exploit a switchable interaction between spins and orbital motion of electrons in silicon quantum dots, without a micromagnet. The weak effects of relativistic spin-orbit interaction in silicon are enhanced, leading to a speed up in Rabi frequency by a factor of up to 650 by controlling the energy quantization of electrons in the nanostructure. Fast electrical control is demonstrated in multiple devices and electronic configurations. Using the electrical drive, we achieve a coherence time T2,Hahn ≈ 50 μs, fast single-qubit gates with Tπ/2 = 3 ns and gate fidelities of 99.93%, probed by randomized benchmarking. High-performance all-electrical control improves the prospects for scalable silicon quantum computing.

Effect of Rashba spin-orbit coupling interaction on energy states of silicon disk-shaped quantum dot

Silicon quantum dots (QDs) are considered an excellent platform for spin qubits due to their weak spin-orbit interaction (SOI). Indeed, due to quantum confinement, novel spin properties arise from the SOI. In this work, we have studied the influence of the Rashba SOI and the confinement potential on the energy spectrum of an electron confined in a Silicon disk-shaped quantum dot, in the presence of an external magnetic field. The effects of the QD size, the confinement potential and the Rashba alpha coefficient on the energy levels are also studied. We used the effective mass approximation to determine the energy levels and their wave functions for different states. The results are presented as a function of the magnetic field in the presence and absence of SOI. We find that the energy levels of the electrons behave very differently depending on the magnetic field. The energy of all states changes with increasing magnetic field and each energy level splits into two and the energy difference between these two levels also increases with magnetic field, in the presence and absence of SOI. The energy levels are proportional to the Rashba alpha coefficient and inversely proportional to the radius of the QD.

Effects of spin-orbit interaction and electron correlations in strontium titanate

We show that the Bloch states in the conduction band of SrTiO$_3$ arise from the interplay between highly anisotropic hopping in sub-bands derived from the Ti $t_{2g}$ orbitals and spin-orbit coupling that mixes these orbitals. Because of the nearly flat-band characteristics for one of the principal axes, at sufficiently high doping these Bloch states become unstable with respect to electron interactions, resulting in Mott-like singlet correlations. These findings may be relevant to the anomalous electronic properties of SrTiO$_3$, including its unusual superconductivity.

Spin-orbit interaction effects on a [formula omitted] complex in a GaAs quantum dot in a magnetic field

The spin-orbit interaction effects on the energetics of a negative donor centre localized in a 3D Gaussian GaAs quantum dot placed in a magnetic field are studied variationally by using a unitary transformation and a Jastrow function to incorporate the role of Coulomb interaction. The Dresselhaus interaction is shown to increase the binding of the negative donor. The diamagnetic susceptibility and the dipole moment of the system are also calculated.

Investigation of semimetallic properties of GdSb and TbSb compounds: A first-principle and optical study

The electronic and optical properties of binary semimetals GdSb and TbSb in the rocksalt cubic structure have been investigated. The spin-polarized band structure calculations were performed within GGA + U method accounting for strong electron correlations in rare-earth ions. The effect of spin-orbit interaction for the band structure is investigated. The resulting band features near the Fermi energy are found in a good agreement with the previous ARPES experimental data. Our first-principle calculations have shown that isostructural compounds GdSb and TbSb are electron-hole compensated semimetals with qualitatively similar electronic structures. A small pseudogap is observed in their densities of states. The energy dependencies of the real and imaginary parts of the complex dielectric permittivity of both materials are investigated by the spectroscopic ellipsometry in the range 0.078–5.6 eV. The experimental optical conductivity spectra are compared with the calculated ones. There is a reasonable agreement between experiment and theory on a number of spectral features formed by quantum transitions and related to the specifics of the electronic structures. The nature of the occurrence of intense absorption bands in the optical conductivity spectra of both compounds has been identified. The anomalous behavior of optical characteristics in the infrared region is associated with the semi-metallic properties of these materials.

Spin-Dependent Electron–Electron Interaction in Rashba Materials

We review the effects of the pair spin-orbit interaction (PSOI) in Rashba materials. The PSOI is the electron-electron interaction component that depends on the spin and momentum of the electrons. Being produced by the Coulomb fields of interacting electrons, it exists already in vacuum, but becomes orders of magnitude larger in materials with the giant Rashba effect. The main nontrivial feature of the PSOI is that it is attractive for electrons in certain spin configurations tied to their momentum and competes with the Coulomb repulsion of the electrons. Under certain conditions attainable in modern low-dimensional structures the PSOI prevails. The resulting attraction between electrons leads to the formation of bound electron pairs, the binding energy of which can be controlled by electrical means. In many-electron systems the PSOI results in the instabilities of the uniform ground state with respect to the density fluctuations, which develop on different spatial scales, depending on the geometry of the electric fields that produce the PSOI. If the PSOI is not too strong the electronic system is stable, but its collective excitations reveal the highly unusual spin-charge structure and spectrum, which manifest themselves in the frequency dependence of the dynamic conductivity.