Spin-orbit Interaction Terms Research Articles

Quantum computing with acceptor spins in silicon

The states of a boron acceptor near a Si/SiO2 interface, which bind two low-energy Kramers pairs, have exceptional properties for encoding quantum information and, with the aid of strain, both heavy hole and light hole-based spin qubits can be designed. Whereas a light-hole spin qubit was introduced recently (arXiv:1508.04259), here we present analytical and numerical results proving that a heavy-hole spin qubit can be reliably initialised, rotated and entangled by electrical means alone. This is due to strong Rashba-like spin–orbit interaction terms enabled by the interface inversion asymmetry. Single qubit rotations rely on electric-dipole spin resonance (EDSR), which is strongly enhanced by interface-induced spin–orbit terms. Entanglement can be accomplished by Coulomb exchange, coupling to a resonator, or spin–orbit induced dipole–dipole interactions. By analysing the qubit sensitivity to charge noise, we demonstrate that interface-induced spin–orbit terms are responsible for sweet spots in the dephasing time as a function of the top gate electric field, which are close to maxima in the EDSR strength, where the EDSR gate has high fidelity. We show that both qubits can be described using the same starting Hamiltonian, and by comparing their properties we show that the complex interplay of bulk and interface-induced spin–orbit terms allows a high degree of electrical control and makes acceptors potential candidates for scalable quantum computation in Si.

Nodal bilayer-splitting controlled by spin-orbit interactions in underdoped high-Tc cuprates.

The highest superconducting transition temperatures in the cuprates are achieved in bilayer and trilayer systems, highlighting the importance of interlayer interactions for high Tc. It has been argued that interlayer hybridization vanishes along the nodal directions by way of a specific pattern of orbital overlap. Recent quantum oscillation measurements in bilayer cuprates have provided evidence for a residual bilayer-splitting at the nodes that is sufficiently small to enable magnetic breakdown tunneling at the nodes. Here we show that several key features of the experimental data can be understood in terms of weak spin-orbit interactions naturally present in bilayer systems, whose primary effect is to cause the magnetic breakdown to be accompanied by a spin flip. These features can now be understood to include the equidistant set of three quantum oscillation frequencies, the asymmetry of the quantum oscillation amplitudes in c-axis transport compared to ab-plane transport, and the anomalous magnetic field angle dependence of the amplitude of the side frequencies suggestive of small effective g-factors. We suggest that spin-orbit interactions in bilayer systems can further affect the structure of the nodal quasiparticle spectrum in the superconducting phase. PACS numbers: 71.45.Lr, 71.20.Ps, 71.18.+y

Photophysics of Singlet and Triplet Intraligand Excited States in [ReCl(CO)3(1-(2-pyridyl)-imidazo[1,5-α]pyridine)] Complexes

Excited-state characters and dynamics of [ReCl(CO)3(3-R-1-(2-pyridyl)-imidazo[1,5-α]pyridine)] complexes (abbreviated ReGV-R, R = CH3, Ph, PhBu(t), PhCF3, PhNO2, PhNMe2) were investigated by pico- and nanosecond time-resolved infrared spectroscopy (TRIR) and excited-state DFT and TD-DFT calculations. Near UV excitation populates the lowest singlet state S1 that undergoes picosecond intersystem crossing (ISC) to the lowest triplet T1. Both states are initially formed hot and relax with ∼20 ps lifetime. TRIR together with quantum chemical calculations reveal that S1 is predominantly a ππ* state localized at the 1-(2-pyridyl)-imidazo[1,5-α]pyridine (= impy) ligand core, with impy → PhNO2 and PhNMe2 → impy intraligand charge-transfer contributions in the case of ReGV-PhNO2 and ReGV-PhNMe2, respectively. T1 is predominantly ππ*(impy) in all cases. It follows that excited singlet and corresponding triplet states have to some extent different characters and structures even if originating nominally from the same preponderant one-electron excitations. ISC occurs with a solvent-independent (CH2Cl2, MeCN) 20-30 ps lifetime, except for ReGV-PhNMe2 (10 ps in CH2Cl2, 100 ps in MeCN). ISC is 200-300 times slower than in analogous complexes with low-lying MLCT states. This difference is interpreted in terms of spin-orbit interaction and characters of orbitals involved in one-electron excitations that give rise to S1 and T1 states. ReGV-R present a unique case of octahedral heavy-metal complexes where the S1 lifetime is long enough to allow for separate spectroscopic characterization of singlet and triplet excited states. This study provides an insight into dynamics and intersystem crossing pathways of low-lying singlet and triplet excited states localized at bidentate ligands bound directly to a heavy metal atom. Rather long (1)IL lifetimes indicate the possibility of photonic applications of singlet excited states.

Bremsstrahlung polarization correlations and their application for polarimetry of electron beams

The correlation between electron spin and photon linear polarization in atomic-field bremsstrahlung was measured with a polarized electron beam. The angle of photon polarization and the photon emission intensity were found to be correlated with the spin orientation. These effects are interpreted in terms of spin-orbit interaction. They lead to a new technique of electron beam polarimetry.

Mechanism of Uniaxial Magnetocrystalline Anisotropy in Transition Metal Alloys

Magnetocrystalline anisotropy in transition metal alloys (FePt, CoPt, FePd, MnAl, MnGa, and FeCo) was studied using first-principles calculations to elucidate its specific mechanism. The tight-binding linear muffin-tin orbital method in the local spin-density approximation was employed to calculate the electronic structure of each compound, and the anisotropy energy was evaluated using the magnetic force theorem and the second-order perturbation theory in terms of spin-orbit interactions. We systematically describe the mechanism of uniaxial magnetocrystalline anisotropy in real materials and present the conditions under which the anisotropy energy can be increased. The large magnetocrystalline anisotropy energy in FePt and CoPt arises from the strong spin-orbit interaction of Pt. In contrast, even though the spin-orbit interaction in MnAl, MnGa, and FeCo is weak, the anisotropy energies of these compounds are comparable to that of FePd. We found that MnAl, MnGa, and FeCo have an electronic structure that is efficient in inducing the magnetocrystalline anisotropy in terms of the selection rule of spin-orbit interaction.

Pseudo-Spin–Orbit Coupling in Graphene within Hydrogenic Impurity Context

In graphene, we report the first theoretical demonstration of how the intrinsic spin orbit interaction can be deduced from the theory and how it can be controlled by tuning a uniform magnetic field, and/or by changing the strength of a long range Coulomb like impurity (adatom), as well as gap parameter. In the impurity context, we find that intrinsic spin-orbit interaction energy may be enhanced by increasing the strength of magnetic field and/or by decreasing the band gap mass term. Additionally, it may be strongly enhanced by increasing the impurity strength. Furthermore, from the proposal of Kane and Mele [Phys. Rev. Lett. 95, 226801 (2005)], it was discussed that the pristine graphene has a quantized spin Hall effect regime where the Rashba type spin orbit interaction term is smaller than that of intrinsic one. Our analysis suggest the nonexistence of such a regime in the ground state of flat graphene.

Breit–Pauli atomic structure calculations for Fe XI

Energy levels, oscillator strengths, and transition probabilities are calculated for the lowest-lying 165 energy levels of Fe XI using configuration-interaction wavefunctions. The calculations include all the major correlation effects. Relativistic effects are included in the Breit–Pauli approximation by adding mass-correction, Darwin, and spin–orbit interaction terms to the non-relativistic Hamiltonian. For comparison with the calculated ab initio energy levels, we have also calculated the energy levels by using the fully relativistic multiconfiguration Dirac–Fock method. The calculated results are in close agreement with the National Institute of Standards and Technology compilation and other available results. New results are predicted for many of the levels belonging to the 3s3p43d and 3s3p33d2 configurations, which are very important in astrophysics, relevant, for example, to the recent observations by the Hinode spacecraft. We expect that our extensive calculations will be useful to experimentalists in identifying the fine structure levels in their future work.

Origin and transport signatures of spin-orbit interactions in one- and two-dimensional SrTiO3-based heterostructures

We study origin of Rashba spin-orbit interaction at SrTiO$_3$ surfaces and LaAlO$_3$/SrTiO$_3$ interfaces by considering the interplay between atomic spin-orbit coupling and inversion asymmetry at the surface or interface. We show that, in a simple tight-binding model involving 3d $t_{2g}$ bands of Ti ions, the induced spin-orbit coupling in the $d_{xz}$ and $d_{yz}$ bands is cubic in momentum whereas the spin-orbit interaction in the $d_{xy}$ band has linear momentum dependence. We also find that the spin-orbit interaction in one-dimensional channels at LaAlO$_3$/SrTiO$_3$ interfaces is linear in momentum for all bands. We discuss implications of our results for transport experiments on SrTiO$_3$ surfaces and LaAlO$_3$/SrTiO$_3$ interfaces. In particular, we analyze the effect of a given spin-orbit interaction term on magnetotransport of LaAlO$_3$/SrTiO$_3$ by calculating weak anti-localization corrections to the conductance and to universal conductance fluctuations.

Metal-insulator transition in three-band Hubbard model with strong spin-orbit interaction

Recent investigations suggest that both spin-orbit coupling and electron correlation play very crucial roles in the 5d transition metal oxides. By using the generalized Gutzwiller variational method and dynamical mean-field theory with the hybridization expansion continuous time quantum Monte Carlo as impurity solver, the three-band Hubbard model with full Hund’s rule coupling and spin-orbit interaction terms, which contains the essential physics of partially filled t 2g sub-shell of 5d materials, is studied systematically. The calculated phase diagram of this model exhibits three distinct phase regions, which are metal, band insulator and Mott insulator. We find that the spin-orbit coupling term tends to greatly enhance the tendency towards the Mott insulator phase. Furthermore, the influence of the electron-electron interaction on the effective strength of spin-orbit coupling in the metallic phase is studied in detail. We conclude that the electron correlation effect on the effective spin-orbit coupling is far beyond the mean-field treatment even in the intermediate coupling region.

Electrical Suppression of Spin Relaxation in GaAs(111)BQuantum Wells

Spin dephasing via the spin-orbit interaction (SOI) is a major mechanism limiting the electron spin lifetime in III-V zincblende quantum wells (QWs). The dephasing can be suppressed in GaAs(111) quantum wells by applying an electric field. The suppression has been attributed to the compensation of the intrinsic SOI associated with the bulk inversion asymmetry of the GaAs lattice by a structural induced asymmetry SOI term induced by an electric field. We provide direct experimental evidence for this mechanism by demonstrating the transition between the bulk inversion asymmetry-dominated to a structural induced asymmetry-dominated regime via photoluminescence measurements carried out over a wide range of applied fields. Spin lifetimes exceeding 100ns are obtained near the compensating electric field, thus making GaAs(111) QWs excellent candidates for the electrical storage and manipulation of spins.

Solutions of Woods—Saxon Potential with Spin-Orbit and Centrifugal Terms through Nikiforov—Uvarov Method

In this study, the analytical solutions of the radial Schrödinger equation for the central Woods—Saxon potential together with spin-orbit interaction and centrifugal terms have been derived by using Nikiforov-Uvarov method. The energy eigenvalues and corresponding eigenfunctions of nucleons have been obtained for various values of n, l, and j quantum numbers. The obtained results using this method are in satisfactory agreement with available data in the special case.

STUDY OF NUCLEAR BOUND STATES USING MEAN-FIELD WOODS–SAXON AND SPIN-ORBIT POTENTIALS

The neutron single-particle bound states as solutions of radial Schrödinger equation for the central Woods–Saxon potential together with spin-orbit interaction and centrifugal terms have been obtained analytically. By introducing new variable and using Taylor expansion, the differential equation has been transformed to solvable hypergeometric type. This differential equation has also been solved using Nikiforov–Uvarov (NU) method. Neutron single-particle states have been derived as self-adjoint form of hypergeometric series. By means of boundary conditions, which implies eigenvalue condition as complicated relation between energy eigenvalues and parameters of nuclear potential, the neutron single-particle energy eigenvalues have been derived using graphical method. To examine method, numerical results in special cases of S states are evaluated. Results obtained using this method are in satisfactory agreements with available numerical solutions.

Breit–Pauli atomic structure calculations for sulphur-like titanium

Configuration interaction calculation has been performed for excitation energies, oscillator strengths, and transition probabilities of 114 fine-structure levels of sulphur-like titanium. The relativistic effects are included in Breit–Pauli approximation by adding mass-correction, Darwin, and spin–orbit interaction terms to the nonrelativistic Hamiltonian. We have adjusted the diagonal elements of Hamiltonian matrices (fine-tuning) before the calculation of oscillator strength and transition probabilities for the electric dipole allowed transitions. Our calculated data are in close agreement with data listed in National Institute of Standards and Technology and other available results. Correct identification of some of the levels become very difficult because of strong mixing among several fine-structure levels. We predict new energy levels, oscillator strength, and transition probability data, where no other theoretical or experimental results are available, which will form the basis for future experimental work.

Gate-controlled persistent spin helix state in (In,Ga)As quantum wells

In layered semiconductors with spin-orbit interaction (SOI) a persistent spin helix (PSH) state with suppressed spin relaxation is expected if the strengths of the Rashba and Dresselhaus SOI terms, $\ensuremath{\alpha}$ and $\ensuremath{\beta}$, are equal. Here we demonstrate gate control and detection of the PSH in two-dimensional electron systems with strong SOI including terms cubic in momentum. We consider strain-free InGaAs/InAlAs quantum wells and first determine a ratio $\ensuremath{\alpha}/\ensuremath{\beta}\ensuremath{\simeq}1$ for nongated structures by measuring the spin-galvanic and circular photogalvanic effects. Upon gate tuning the Rashba SOI strength in a complementary magnetotransport experiment, we monitor the complete crossover from weak antilocalization via weak localization to weak antilocalization, where the emergence of weak localization reflects a PSH-type state. A corresponding numerical analysis reveals that such a PSH-type state indeed prevails even in presence of strong cubic SOI, however no longer at $\ensuremath{\alpha}=\ensuremath{\beta}$.

Computation of relativistic terms in a spherical quantum dot

We studied a hydrogenic impurity located at the center of a spherical quantum dot with an infinite spherical confining potential and calculated energy levels and wavefunctions using Quantum Genetic Algorithm(QGA) and Hartree–Fock Roothaan (HFR) method. In addition, we investigated the first-order relativistic terms such as the relativistic correction to the kinetic energy, Darwin and spin–orbit interaction term. These terms were calculated using the first-order perturbation theory. The electronic charge density for the Darwin term was carried out from a global operator defined by Hiller, Sucher and Feinberg. The results revealed that the relativistic corrections are important in small dot radii and they should not be neglected to improve the accuracy of calculations.

't Hooft Quantization for Interacting Systems

In the framework of 't Hooft's "deterministic quantization" proposal, we show how to obtain from a composite system of two classical Bateman's oscillators a quantum isotonic oscillator. In a specific range of parameters, such a system can be also interpreted as a particle in an effective magnetic field, interacting through a spin-orbit interaction term. In the limit of a large separation from the interaction region, the system can be described in terms of two irreducible elementary subsystems, corresponding to two independent quantum harmonic oscillators.

Microscopic theory on the Gilbert damping due to spin pumping effects in the magnetic multi-layer system

We have calculated the Gilbert damping coefficient α in the magnetic multi-layer structures consisted of ferromagnetic (FM) and non-magnetic (NM) layers which are FM/NM and FM/NM/FM from microscopic theory. In this study, our model Hamiltonian doesn't include the spin-orbit interaction term, but the kinetic electron hopping term. For obtaining α in theory, we used Kubo formula and Projection method. We found α is dependent on structure of systems and both thickness of the FM and NM layer. Spin pumping effect which is predicted by experimental results is confirmed by this calculation in theory. We conclude that transferring conduction electrons carrying angular momentum to adjacent layers are the origin of the Gilbert damping for multi-layer systems.

Transport properties of low-dimensional semiconductor structures in the presence of spin–orbit interaction

Transport properties of a two-dimensional electron gas (2DEG) and of quantum wires are theoretically studied in the presence of both Rashba and Dresselhaus terms of the spin–orbit interaction (SOI). Fully quantum mechanical expressions for the conductivity are evaluated for very low temperatures and the differences between them and previous semiclassical results are highlighted. Two kinds of confining potentials in quantum wires are considered, square-type and parabolic. Various cases depending on the relative strengths of two different SOI terms are discussed and the relaxation times for various impurity potentials are evaluated. In addition, the spin accumulation in a 2DEG and in a quantum wire (QW) is evaluated semiclassically and its dependence on the Fermi energy and the SOI strengths is discussed. A nearly saw-tooth dependence on the electron concentration is obtained for a QW with parabolic confinement.

New atomic data for Ti X

A large-scale configuration interaction (CI) calculation using CIV3 is performed for the 303 fine-structure levels of the aluminum-like titanium ion. We have calculated the energy levels, oscillator strengths, and transition probabilities for the electric dipole allowed and intercombination transitions among the levels of ground state 3s 23p ( 2p o) and higher energy levels of states 3s3p 2, 3p 3, 3s3p3d, 3p 23d, 3s 24s, 3s3d 2, 3s 24p, 3s3p4s, 3s3p4p, 3p3d 2, 3s3p4d, 3s3p4f, 3s 25p, 3p 24p, 3s3d4s, 3s3p5s, 3s3d4p, 3s3p5p, 3s 2(4d, 4f, 5s, 5d, 5f, 6s, 6p, 6d, 6f) of Ti X in the LSJ coupling scheme. The calculations include all the major correlation effects. We attempt to correct the inaccuracies in the CI coefficients in the wavefunctions, which would lead to inaccuracies in transition probabilities by applying a “fine-tuning” technique. The relativistic effects are incorporated by adding the mass correction, Darwin, and spin–orbit interaction terms into the non-relativistic Hamiltonian in the Breit–Pauli approximation. The present results are in good agreement with other available calculations and experiments. Several new lines corresponding to 3s3p nl ( n = 4, 5 and l = 0, 1), 3s 25p, 3s 2(6s, 6p) and other configurations are predicted where no other theoretical or experimental results are available. We expect that our extensive calculations will be useful to experimentalists in identifying the fine-structure levels in their future work.

Lifetime for the Ti X spectrum

We present configuration interaction calculations for the lifetime of 294 fine-structure levels of the Ti X spectrum in the LSJ coupling scheme. The calculations include all the major correlation effects. The relativistic effects are included by adding the mass correction term, Darwin term and spin–orbit interaction term to the non-relativistic Hamiltonian in the Breit–Pauli approximation. The calculated lifetime values are in very close agreement with other available experimental and theoretical results. We have predicted new lifetime results for levels belonging to 3p23d, 3s24p, 3s3p4s, 3s3p4p and various other configurations of Ti X, where no other theoretical and experimental results are available.