Spin texture and Berry phase of heavy-mass holes confined in SiGe two-dimensional quantum well system under the coexistence of Rashba and Dresselhaus spin-orbit interactions

We study the spin texture (ST) and Berry phase (BP) of heavy-mass holes (HHs) confined in the SiGe two-dimensional quantum well system, focusing on the coexistence of Rashba (R) and Dresselhaus (D) spin-orbit interactions (SOIs). We extend DKK's k.p perturbation approach by take into account the R- and D-relating SOIs up to the 2nd-order terms crossing with k.p term, and computationally explore ST and BP. The coexistence of both types of SOIs removes the C₄ symmetry from ST, and the C₂ symmetry results. The R-SOI orients spin to the tangential direction of the equi-energy surface, whereas the D-SOI causes the directional discrepancy from the contour line.

We then calculate the energy (E) dependent BP (γ^HH+/-) for the spin-stabilized/destabilized HH. γ^HH+/- causes the plateau having a value of +/-π in the lower E region. However, with an increase in E, γ^HH+/- abruptly changes its sign due to the R-SOI and angular momenta |l|=1. We further study the temperature (T) dependent BP (<γ^HH+/->) by employing thermal averaging. <γ^HH+/-> shows also the +/-π plateau at low T, and then changes its sign into an opposite around 200K. These characteristics are understandable by counting the number of quasi-degenerate points with the sign of BP.