Zitterbewegung of a heavy hole in presence of spin-orbit interactions

Abstract

We study the zitterbewegung of a heavy hole in presence of both cubic Rashba and cubic Dresselhaus spin-orbit interactions. On contrary to the electronic case, zitterbewegung does not vanish for equal strength of Rashba and Dresselhaus spin-orbit interaction. This non-vanishing of zitterbewegung is associated with the Berry phase. Due to the presence of the spin-orbit coupling the spin associated with the heavy hole precesses about an effective magnetic field. This spin precession produces a transverse spin-orbit force which also generates an electric voltage associated with zitterbewegung. We have estimated the magnitude of this voltage for a possible experimental detection of zitterbewegung.

Spin-orbit interactions in inversion-asymmetric two-dimensional hole systems: A variational analysis

“…4,6,7,27,32,[36][37][38][39][40][41] However, we demonstrate that the validity of the SW-transformed model is limited to a relatively narrow range of parameters, indicating that in general the HH spin splitting contains higher-order terms in the wave vector, which are frequently sizeable. The limited applicability of the simple dispersion relation to realistic heterostructures is relevant to the current understanding of the spin-Hall conductivity, 32,37,39,52 hole spin helix, 40 and Zitterbewegung, 38,41 all of which have been derived based on the assumption that the HH spin splitting is proportional to k 3 .…”

“…In the axial approximation, i.e., ignoring anisotropic corrections including warping and BIA, the SW transformation enables one to write the dispersion relation in a rather simple form E ± (k) = Ak 2 − Bk 4 ± Ck 3 where A, B, and C are material-and structure-dependent coefficients, and the Ck 3 term represents the Rashba spin splitting. 4,6,7,27,32,[36][37][38][39][40][41] However, we demonstrate that the validity of the SW-transformed model is limited to a relatively narrow range of parameters, indicating that in general the HH spin splitting contains higher-order terms in the wave vector, which are frequently sizable. The limited applicability of the simple dispersion relation to realistic heterostructures is relevant to the current understanding of the spin-Hall conductivity, 32,37,39,52 hole spin helix, 40 and Zitterbewegung, 38,41 all of which have been derived based on the assumption that the HH spin splitting is proportional to k 3 .…”

“…GaAs inversion layers with N D − N A = 3 × 10 20 m −3 and densities p < 2.5 × 10 15 m −2 , there are many parameter regimes in which SW breaks down. The fact that the simple dispersion can fail for realistic parameters challenges the current theories on electric dipole spin resonance (EDSR), 55 spin conductivity, 32,37,39,52 hole spin helix, 40 and Zitterbewegung, 38,41 which assume that hole spin-orbit coupling is simply cubic in wave vector.…”

“…Inversion asymmetry in semiconductor heterostructures may stem from the asymmetry of the confining potential [structural inversion asymmetry (SIA) or Rashba terms 28 ] or from the asymmetry of the underlying crystal structure [bulk inversion asymmetry (BIA) or Dresselhaus terms 29 ]. BIA and SIA spin splittings are proportional to odd powers of k, with k-linear 6,[30][31][32][33][34][35] and k 3 terms 4,6,7,27,29,32,[35][36][37][38][39][40][41] frequently representing the dominant contributions. They result in a high degree of nonparabolicity of the hole energy bands.…”

Generating a topological anomalous Hall effect in a non-magnetic conductor

“…Since the equilibrium system is not magnetized the effect is tunable in situ by altering the magnetic field orientation. It is observable in state-of-theart hole samples, which are developing at a brisk pace, motivated in part by quantum computing applications [40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57], where holes are actively investigated [58][59][60], by their large spin-orbit coupling [61][62][63], interesting transport properties [64][65][66][67][68], and by unconventional properties stemming from their spin-3/2 nature [69][70][71][72][73][74][75][76][77][78][79][80][81][82]. We consider a two-dimensional hole gas grown along (113).…”