Spin relaxation dynamics of quasiclassical electrons in ballistic quantum dots with strong spin-orbit coupling

Abstract

We performed path integral simulations of spin evolution controlled by the Rashba spin-orbit interaction in the semiclassical regime for chaotic and regular quantum dots. The spin polarization dynamics have been found to be strikingly different from the D'yakonov-Perel' (DP) spin relaxation in bulk systems. Also an important distinction have been found between long time spin evolutions in classically chaotic and regular systems. In the former case the spin polarization relaxes to zero within relaxation time much larger than the DP relaxation, while in the latter case it evolves to a time independent residual value. The quantum mechanical analysis of the spin evolution based on the exact solution of the Schrödinger equation with Rashba SOI has confirmed the results of the classical simulations for the circular dot, which is expected to be valid in general regular systems. In contrast, the spin relaxation down to zero in chaotic dots contradicts to what have to be expected from quantum mechanics. This signals on importance at long time of the mesoscopic echo effect missed in the semiclassical simulations. I INTRODUCTIONSpin relaxation in semiconductors is an important physical phenomenon being actively studied recently in connection with various spintronics applications [1]. In doped bulk samples and quantum wells (QW) of III-V semiconductors at low temperatures spin relaxation is mostly due to the DP mechanism [2]. This mechanism does not involve any inelastic processes, so that the exponential decay of the spin polarization is determined entirely by the spin-orbit interaction (SOI) and elastic scattering of electrons on the impurities. However, in case of confined systems such as quantum dots (QD) with atomic-like eigenstates, the SOI has been incorporated into the structure of the wave functions of the discrete energy levels. Without inelastic interactions, an initial wave packet with a given spin polarization will evolve in time as a coherent superposition of these discrete eigenstates. Therefore, the corresponding expectation value of the spin polarization will oscillate in time without any decay. To obtain a polarization decay in the QD's, extra effects have to be introduced into the system, e.g., the inelastic interactions between electrons and phonons mediated by the spin-orbit [3,4] and nuclear hyperfine effects [3,5,6]. Accordingly, a spin relaxation in QD's induced by these effects is a real dephasing process.Unlike such an inelastic relaxation in QD's, the DP spin relaxation in unbounded systems seems to be a quite different phenomenon, because the scattering on impurities is elastic and there is no dephasing of the electron wave functions in the systems. However, the spin polarization does decay in time exponentially, as if it would be a true dephasing process. To explain this phenomenon, let us consider an electron moving diffusively through an unbounded system with random elastic scatters. This electron is described by a wave packet represented by a superposition of continuum eigenstates. During a ...

Spin relaxation in narrow wires of a two-dimensional electron gas

“…[5][6][7][8][9][10] This effect can be traced back to the specific form of the spin-orbit field in the Rashba Hamiltonian-being proportional to the velocity. 7 Here we formulate the argument for a system including Rashba and also linear Dresselhaus term within the spin-diffusion equation approach.…”

“…The maximum spin relaxation time occurs when the width is of the order of the bulk spin relaxation length. Remarkably, while the tendency to suppress spin relaxation in confined systems has been predicted in a number of theoretical works, [4][5][6][7][8][9][10] there has been no anticipation of the increase of the spin relaxation observed at the smallest widths. In this paper we show that spin active boundaries, not considered in the previous theoretical analysis, dramatically change the size dependence of the spin relaxation time in the small width limit and provide a useful point of view as far as the interpretation of the experiment is concerned.…”

Imaging mesoscopic spin Hall flow: Spatial distribution of local spin currents and spin densities in and out of multiterminal spin-orbit coupled semiconductor nanostructures

“…On the other hand, the presence of SO couplings makes the dynamics of transported spin in experimentally relevant confined structures strongly dependent on the properties of their interfaces, boundaries, and the attached electrodes, 53 even for semiclassical spatial propagation of charges which carry spins evolving according to quantum dynamical laws. 56 For example, heuristic arguments based on the Keldysh formalism applied to an infinite two-terminal structure (lacking actual lateral edges) of Ref. 27 suggest that nonequilibrium spin Hall accumulation S z m = 0 will appear only in the four corners at the lead/2DEG interfaces (due to J z y = 0 existing within a spin relaxation length L SO wide region around such interfaces), in contrast to the Keldysh formalism applied to finite-size 2DEG in the Landauer two-terminal setup where non-zero spin accumulation (with opposite sign on the two lateral edges 1,2 ) is found along the whole lateral edge.…”

Edge effects in graphene nanostructures: From multiple reflection expansion to density of states

“…46 Related trace formulas appear also in trajectory-based treatments of electronic systems with spin-orbit interaction. [47][48][49][50] We note that semiclassical methods have also been used to study graphene in magnetic fields. [51][52][53] Following the concepts outlined above we address edge effects on the electronic spectra of closed graphene cavities and quantum transport through open graphene systems in two consecutive papers.…”