Superconducting phase with a chiral $f$-wave pairing symmetry and Majorana fermions induced in a hole-doped semiconductor

TL;DR

This paper proposes a method to induce chiral $f+if$-wave superconductivity in a hole-doped semiconductor via proximity effect, leading to Majorana fermions and edge states, with potential applications in topological quantum computing.

Contribution

It demonstrates the induction of chiral $f+if$-wave pairing and Majorana fermions in a hole-doped semiconductor, a novel approach for topological superconductivity.

Findings

Chiral $f+if$-wave pairing can be induced via proximity effect.

Existence of three chiral Majorana edge states.

Zero energy Majorana fermions found in vortices.

Abstract

We show that a chiral $f+if$-wave superconducting pairing may be induced in the lowest heavy hole band of a hole-doped semiconductor thin film through proximity contact with an \textit{s}-wave superconductor. The chirality of the pairing originates from the $3\pi $ Berry phase accumulated for a heavy hole moving along a close path on the Fermi surface. There exist three chiral gapless Majorana edge states, in consistence with the chiral $f+if$% -wave pairing. We show the existence of zero energy Majorana fermions in vortices in the semiconductor-superconductor heterostructure by solving the Bogoliubov-de-Gennes equations numerically as well as analytically in the strong confinement limit.