Spin Textures and Berry Phases for Holes Confined in SiGe Mixed-Alloy 2D Quantum Well System: Quantization of Berry Phase via Intersubband Interaction

In their last article [Phys. Lett. A 2021, 389, 127091], the authors have extended the (Formula presented.) approach by considering crossings with the spin–orbit interaction (SOI) up to the second order and studied the spin texture and Berry phase of the heavy-mass holes (HHs) confined in the SiGe 2D quantum well system. HHs cause quasi-degeneracy via the intersub-band interaction (ISI) working as Dirac-like singularity, leading to the energy-dependent Berry phase “quantized” by π. This π quantization is understandable by counting the number of quasi-degenerate points in the Brillouin zone alongside recognizing the sign of the Berry curvature there. Herein, the remaining holes of the light-mass holes (LHs) and separate holes (SHs) are studied. The spin textures and the Berry curvatures and phases are explored comprehensively, focusing on the competition between the Rashba and Dresselhaus SOIs via ISI. Comparisons with HHs elucidate that LHs and SHs cause similar quasi-degeneracy through ISI, functioning as the Dirac-like singularity. As such, the Berry phase is quantized by π, confirming the validity of the counting model irrespective of hole type. In some peculiar cases, HHs and LHs cause a possible sign inversion in the Berry phase, leading to zero Berry phase against temperature.