Majorana Fermions in Ge/Si Hole Nanowires

TL;DR

This paper models Ge/Si core/shell nanowires with hole states coupled to superconductors, demonstrating conditions for Majorana fermions with tunable localization lengths influenced by electric and magnetic fields.

Contribution

It provides a microscopic model incorporating material-specific band structure details, including Rashba spin-orbit interaction and g-factor anisotropy, to analyze Majorana fermions in nanowires.

Findings

Majorana fermions' localization depends on field directions and magnitudes.

Optimal field regimes maximize Majorana localization at nanowire ends.

Oscillations in fermion energy splitting reveal spin-orbit and g-factor properties.

Abstract

We consider Ge/Si core/shell nanowires with hole states coupled to an $s$-wave superconductor in the presence of electric and magnetic fields. We employ a microscopic model that takes into account material-specific details of the band structure such as strong and electrically tunable Rashba-type spin-orbit interaction and $g$ factor anisotropy for the holes. In addition, the proximity-induced superconductivity Hamiltonian is derived starting from a microscopic model. In the topological phase, the nanowires host Majorana fermions with localization lengths that depend strongly on both the magnetic and electric fields. We identify the optimal regime in terms of the directions and magnitudes of the fields in which the Majorana fermions are the most localized at the nanowire ends. In short nanowires, the Majorana fermions hybridize and form a subgap fermion whose energy is split away from zero and oscillates as a function of the applied fields. The period of these oscillations could be used to measure the dependence of the spin-orbit interaction on the applied electric field and the $g$ factor anisotropy.