Low-energy subband wave-functions and effective $g$-factor of one-dimensional hole gas

TL;DR

This paper analytically investigates the low-energy wave-functions and effective g-factors of a one-dimensional hole gas in a cylindrical Ge nanowire, revealing the role of orbital effects and the behavior of g-factors near the center of momentum space.

Contribution

It provides exact solutions for the low-energy subband wave-functions and analyzes the magnetic field effects on the effective g-factor, including orbital contributions and their variation with momentum.

Findings

Degenerate subbands related by time-reversal and spin-rotation.

Orbital effects significantly influence the effective g-factor.

Sharp features in g-factor near the center of k-space.

Abstract

One-dimensional (1D) hole gas confined in a cylindrical Ge nanowire has potential applications in quantum information technologies. Here, we analytically study the low-energy properties of this 1D hole gas. The subbands of the hole gas are two-fold degenerate. The low-energy subband wave-functions are obtained exactly, and the degenerate pairs are related to each other via a combination of the time-reversal and the spin-rotation transformations. In evaluating the effective $g$-factor of these low-energy subbands, the orbital effects of the magnetic field are shown to contribute as strongly as the Zeeman term. Also, near the center of the $k_{z}$ space, there is a sharp dip or a sharp peak in the effective $g$-factor. At the site $k_{z}=0$, the longitudinal $g$-factor $g_{l}$ is much less than the transverse $g$-factor $g_{t}$ for the lowest subband, while away from the site $k_{z}=0$, $g_{l}$ can be comparable to $g_{t}$.