Majorana zero modes in gate-defined germanium hole nanowires

TL;DR

This paper theoretically investigates gate-defined germanium hole nanowires as a promising platform for realizing Majorana zero modes, analyzing conditions for topological phases and the effects of various parameters.

Contribution

It introduces a detailed theoretical model for Ge hole channels, showing they can host Majorana zero modes under certain conditions, advancing potential quantum computing applications.

Findings

Narrow Ge hole channels can enter topological superconducting phases.

Topological gap size depends on channel width, strain, and electric field.

Ge hole channels may overcome disorder issues in Majorana platforms.

Abstract

We theoretically study gate-defined one-dimensional channels in planar Ge hole gases as a potential platform for non-Abelian Majorana zero modes. We model the valence band holes in the Ge channel by adding appropriate confinement potentials to the 3D Luttinger-Kohn Hamiltonian, additionally taking into account a magnetic field applied parallel to the channel, an out-of-plane electric field, as well as the effect of compressive strain in the parent quantum well. Assuming that the Ge channel is proximitized by an $s$-wave superconductor (such as, e.g., Al) we calculate the topological phase diagrams for different channel geometries, showing that sufficiently narrow Ge hole channels can indeed enter a topological superconducting phase with Majorana zero modes at the channel ends. We estimate the size of the topological gap and its dependence on various system parameters such as channel width, strain, and the applied out-of-plane electric field, allowing us to critically discuss under which conditions Ge hole channels may manifest Majorana zero modes. Since ultra-clean Ge quantum wells with hole mobilities exceeding one million and mean-free paths on the order of many microns already exist, gate-defined Ge hole channels may be able to overcome some of the problems caused by the presence of substantial disorder in more conventional Majorana platforms.