Phonon-induced Spin Relaxation Research Articles

Many-body theory of phonon-induced spin relaxation and decoherence

First-principles calculations enable accurate predictions of electronic interactions and dynamics. However, computing the electron spin dynamics remains challenging. The spin-orbit interaction causes various dynamical phenomena that couple with phonons, such as spin precession and spin-flip e-ph scattering, which are difficult to describe with current first-principles calculations. In this work, we show a rigorous framework to study phonon-induced spin relaxation and decoherence, by computing the spin-spin correlation function and its vertex corrections due to e-ph interactions. We apply this approach to a model system and develop corresponding first-principles calculations of spin relaxation in GaAs. Our vertex-correction formalism is shown to capture the Elliott-Yafet, Dyakonov-Perel, and strong-precession mechanisms - three independent spin decoherence regimes with distinct physical origins - thereby unifying their theoretical treatment and calculation. Our method is general and enables quantitative studies of spin relaxation, decoherence, and transport in a wide range of materials and devices.

Finite-Size Effect in Phonon-Induced Elliott-Yafet Spin Relaxation in Al.

The Elliott-Yafet theory of spin relaxation in nonmagnetic metals predicts proportionality between spin and momentum relaxation times for scattering centers such as phonons. Here, we test this theory in Al nanowires over a very large thickness range (8.5-300nm), finding that the Elliott-Yafet proportionality "constant" for phonon scattering in fact exhibits a large, unanticipated finite-size effect. Supported by analytical and numerical modeling, we explain this via strong phonon-induced spin relaxation at surfaces and interfaces, driven in particular by enhanced spin-orbit coupling.

Electrical control of a spin qubit in InSb nanowire quantum dots: Strongly suppressed spin relaxation in high magnetic field

In this paper, we investigate the impact of gating potential and magnetic field on phonon induced spin relaxation rate and the speed of the electrically driven single-qubit operations inside the InSb nanowire spin qubit. We show that a strong $g$ factor and high magnetic field strength lead to the prevailing influence of electron-phonon scattering due to deformation potential, considered irrelevant for materials with a weak $g$ factor, like GaAs or Si/SiGe. In this regime, we find that spin relaxation between qubit states is significantly suppressed due to the confinement perpendicular to the nanowire axis. We also find that maximization of the number of single-qubit operations that can be performed during the lifetime of the spin qubit requires single quantum dot gating potential.

Control of a spin qubit in a lateral GaAs quantum dot based on symmetry of gating potential

We study the influence of quantum dot symmetry on the Rabi frequency and phonon induced spin relaxation rate in a single electron GaAs spin qubit. We find that anisotropic dependence on the magnetic field direction is independent of the choice of the gating potential. Also, we discover that relative orientation of the quantum dot, with respect to the crystallographic frame, is relevant in systems with ${\bf C}_{1{\rm v}}$, ${\bf C}_{2{\rm v}}$, or ${\bf C}_{n}$ ($n\neq4r$) symmetry. To demonstrate the important impact of the gating potential shape on the spin qubit lifetime, we compare the effects of an equilateral triangle, square, and rectangular confinement with the known results for the harmonic potential. In the studied cases, enhanced spin qubit lifetime is revealed, reaching almost six orders of magnitude increase for the equilateral triangle gating.

Spin-relaxation anisotropy in a nanowire quantum dot with strong spin-orbit coupling

We study the impacts of the magnetic field direction on the spin-manipulation and the spin-relaxation in a one-dimensional quantum dot with strong spin-orbit coupling. The energy spectrum and the corresponding eigenfunctions in the quantum dot are obtained exactly. We find that no matter how large the spin-orbit coupling is, the electric-dipole spin transition rate as a function of the magnetic field direction always has a π periodicity. However, the phonon-induced spin relaxation rate as a function of the magnetic field direction has a π periodicity only in the weak spin-orbit coupling regime, and the periodicity is prolonged to 2π in the strong spin-orbit coupling regime.

Simultaneous Spin-Charge Relaxation in Double Quantum Dots

We investigate phonon-induced spin and charge relaxation mediated by spin-orbit and hyperfine interactions for a single electron confined within a double quantum dot. A simple toy model incorporating both direct decay to the ground state of the double dot and indirect decay via an intermediate excited state yields an electron spin relaxation rate that varies nonmonotonically with the detuning between the dots. We confirm this model with experiments performed on a GaAs double dot, demonstrating that the relaxation rate exhibits the expected detuning dependence and can be electrically tuned over several orders of magnitude. Our analysis suggests that spin-orbit mediated relaxation via phonons serves as the dominant mechanism through which the double-dot electron spin-flip rate varies with detuning.

Analysis of phonon-induced spin relaxation processes in silicon

We study all of the leading-order contributions to spin relaxation of conduction electrons in silicon due to the electron-phonon interaction. Using group theory, the $k\ifmmode\cdot\else\textperiodcentered\fi{}p$ perturbation method, and the rigid-ion model, we derive an extensive set of matrix element expressions for all of the important spin-flip transitions in the multivalley conduction band. The scattering angle has an explicit dependence on the electron wave vectors, phonon polarization, valley position, and spin orientation of the electron. Comparison of the derived analytical expressions with results of empirical pseudopotential and adiabatic band charge models shows excellent agreement.

Spin-phonon coupling in single Mn-doped CdTe quantum dot

The spin dynamics of a single Mn atom in a laser driven CdTe quantum dot is addressed theoretically. Recent experimental results\cite{Le-Gall_PRL_2009,Goryca_PRL_2009,Le-Gall_PRB_2010}show that it is possible to induce Mn spin polarization by means of circularly polarized optical pumping. Pumping is made possible by the faster Mn spin relaxation in the presence of the exciton. Here we discuss different Mn spin relaxation mechanisms. First, Mn-phonon coupling, which is enhanced in the presence of the exciton. Second, phonon-induced hole spin relaxation combined with carrier-Mn spin flip coupling and photon emission results in Mn spin relaxation. We model the Mn spin dynamics under the influence of a pumping laser that injects excitons into the dot, taking into account exciton-Mn exchange and phonon induced spin relaxation of both Mn and holes. Our simulations account for the optically induced Mn spin pumping.

Theory of the Spin Relaxation of Conduction Electrons in Silicon

A realistic pseudopotential model is introduced to investigate the phonon-induced spin relaxation of conduction electrons in bulk silicon. We find a surprisingly subtle interference of the Elliott and Yafet processes affecting the spin relaxation over a wide temperature range, suppressing the significance of the intravalley spin-flip scattering, previously considered dominant, above roughly 120 K. The calculated spin relaxation times T1 agree with the spin resonance and spin injection data, following a T(-3) temperature dependence. The valley anisotropy of T1 and the spin relaxation rates for hot electrons are predicted.

Spin relaxation and g-factor manipulation in quantum dots

Phonon-induced spin relaxation rates and electron g-factor tuning of quantum dots are studied as function of in-plane and perpendicular magnetic fields for different dot sizes. We consider Rashba and Dresselhaus spin-orbit mixing in wide and narrow-gap semiconductors, and show how Zeeman sublevels can relax via piezoelectric (GaAs) and deformation (InSb) potential coupling to acoustic phonons. We find that strong confinement may induce minima in the rates at particular values of the magnetic field (due to a magnetic field-induced cancellation of the spin-orbit effects), where spin relaxation times can reach seconds. We also report on g-factor anisotropy. We obtain good agreement with available experimental values.

Theory of Phonon-Induced Spin Relaxation in Laterally Coupled Quantum Dots

Phonon-induced spin relaxation in coupled lateral quantum dots in the presence of spin-orbit coupling is calculated. The calculation for single dots is consistent with experiment. Spin relaxation in double dots at useful interdot couplings is dominated by spin-hot spots that are strongly anisotropic. Spin-hot spots are ineffective for a diagonal crystallographic orientation of the dots with a transverse in-plane field. This geometry is proposed for spin-based quantum information processing.

Spin relaxation in a GaAs quantum dot embedded inside a suspended phonon cavity

The phonon-induced spin relaxation in a two-dimensional quantum dot embedded inside a semiconductor slab is investigated theoretically. An enhanced relaxation rate is found due to the phonon van Hove singularities. Oppositely, a vanishing deformation potential may also result in a suppression of the spin relaxation rate. For larger quantum dots, the interplay between the spin orbit interaction and Zeeman levels causes the suppression of the relaxation at several points. Furthermore, a crossover from confined to bulklike systems is obtained by varying the width of the slab.

Oscillatory spin relaxation rates in quantum dots

Phonon-induced spin relaxation rates in quantum dots are studied as function of in-plane and perpendicular magnetic fields, temperature and electric field, for different dot sizes. We consider Rashba and Dresselhaus spin-orbit mixing in diferent materials, and show how Zeeman sublevels can relax via piezoelectric and deformation potential coupling to acoustic phonons. We find that strong lateral and vertical confinements may induce minima in the rates at particular values of the magnetic field, where spin relaxation times can reach even seconds. We obtain good agreement with experimental findings in GaAs quantum dots.

Electron–phonon-induced spin relaxation in InAs quantum dots

We have calculated spin-relaxation rates in parabolic quantum dots due to the phonon modulation of the spin–orbit interaction in the presence of an external magnetic field. Both deformation potential and piezoelectric electron–phonon coupling mechanisms are included within the Pavlov–Firsov spin–phonon Hamiltonian. Our results have demonstrated that, in narrow gap materials, the electron–phonon deformation potential and piezoelectric coupling give comparable contributions to spin-relaxation processes. For large dots, the deformation potential interaction becomes dominant. This behavior is not observed in wide or intermediate gap semiconductors, where the piezoelectric coupling, in general, governs the spin-relaxation processes. We have also demonstrated that spin-relaxation rates are particularly sensitive to the Landé g-factor.

Phonon-Induced Spin Relaxation of Conduction Electrons in Aluminum

Spin-flip Eliashberg function ${\ensuremath{\alpha}}_{S}^{2}F$ and temperature-dependent spin relaxation time ${T}_{1}(T)$ are calculated for aluminum using realistic pseudopotentials. The spin-flip electron-phonon coupling constant ${\ensuremath{\lambda}}_{S}$ is found to be $2.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$. The calculations agree with experiments validating the Elliott-Yafet theory and the spin-hot-spot picture of spin relaxation for polyvalent metals.

Investigation of the Temperature Dependence of the Conduction Electron Spin Resonance Parameters in Silver with Many-Body Effects andgAnisotropy

Temperature dependence of the g value, linewidth and peak height of the conduction electron spin resonance in silver has been investigated with the transmission method at the frequency of 22.7 GHz over the temperature range 1.7 to 43 K. We have observed a g shift at the highest temperatures due to the positive exchange coupling larger than g anisotropy, in accordance with the theoretical model by Freedman and Fredkin (1975). Phonon-induced spin relaxation has been found to be proportional to the phonon-induced momentum relaxation of electrons.

Combined Effects of Impurity and Thickness on the Conduction Electron Spin Resonance Linewidth in Silver

The conduction electron spin resonance of silver foils doped with 10 ppm Au has been measured by the transmission method over the thickness range 5-66 µm in the temperature range between 18 K and 44 K at 22.7 GHz as functions of thickness and temperature. As a result of doping silver with Au, the spin-orbit parameter dominating the phonon-induced spin relaxation has not been changed significantly. On the other hand, the surface spin scattering probability e has increased from 6×10 -4 to 2×10 -3 . This increase with Au impurities has been attributed to the impurity-induced disorder of the silver surface.

Conduction-electron-spin-resonance linewidth in cold-worked aluminum

A spin-flip mechanism recently proposed by Silsbee and Beuneu to explain the phonon-induced spin relaxation in Al can also account for the conduction-electron-spin-resonance linewidth induced by dislocations in cold-worked Al.