Spin-orbit coupling effects on the band strucutre of prismatic core/shell nanowires

Core/shell nanowires (CSNWs) exhibit strong radial confinement of electrons within the shell, often leading to a description as a two-dimensional electron gas. We study three-dimensional electron gases within the shell of CSNWs with realistic, polygonal cross-sections. This cross-sectional geometry is determined by the underlying crystal structure, and is unique for specific growth directions. For zinc-blende nanowires grown along the [111] direction, the cross-section may be hexagonal or triangular, whereas for the [001] direction they may be square. Sharp corners in the cross-sections introduce an extra level of confinement, beyond the radial confinement, due to discrete rotational symmetry. The confinement forces the probability density of low energy states to be restricted to the corners of the polygon. For lower symmetry cross-sections, this results in large gaps in the conduction band structure between states confined in the corners and those which have peak probability in the sides of the cross-section. Our study focuses on conduction electrons within thin shells of CSNWs, the energies and eigenstates of which are determined using an exact diagonalization scheme. We present the probability densities and band structures for conduction electrons in the shell of circular, hexagonal, square, and triangular CSNWs. The model includes effective forms of spin-orbit coupling and the inclusion of external magnetic fields.