Hole subband dispersions and strong `spin'-orbit coupling in a cylindrical Ge nanowire

Abstract

Quasi-one-dimensional hole gas is achievable in a semiconductor Ge nanowire. The lowest two subband dispersions of the hole gas are just two shifted parabolic curves with an anticrossing at $k_z=0$. This peculiar low-energy subband structure manifests the existence of a strong `spin' (pseudo spin)-orbit coupling. Based on the Luttinger-Kohn Hamiltonian in the axial approximation, we show two sets of combined dispersions that not only isolated from each other but also with strong `spin'-orbit coupling are obtainable in the presence of strong magnetic field. Realistic calculations are performed for three representative nanowire growth directions [001], [111], and [110]. These results are further confirmed via constructing the low-energy effective Hamiltonian of the hole gas. We also calculate the external electric field induced spin splitting for comparison with the magnetic field induced spin splitting.

17 pages, 17 figures. Published version