Topological minigap in quasi-one-dimensional spin-orbit-coupled semiconductor Majorana wires

TL;DR

This paper investigates the behavior of the minigap in quasi-one-dimensional spin-orbit-coupled semiconductor wires hosting Majorana modes, revealing conditions under which the minigap can vanish and proposing methods to restore it for better experimental detection.

Contribution

It demonstrates how approximate chiral symmetry affects the minigap in multi-band wires and proposes breaking this symmetry with a second Zeeman field to maintain a finite minigap.

Findings

Minigap can vanish when Zeeman field exceeds half the confinement-induced bandgap.

Applying a second Zeeman field breaks chiral symmetry and restores the minigap.

The behavior of the minigap differs from idealized p-wave superconductor models.

Abstract

The excitation gap above the Majorana fermion (MF) modes at the ends of 1D topological superconducting (TS) semiconductor wires scales with the bulk quasiparticle gap E_{qp}. This gap, also called minigap, facilitates experimental detection of the pristine TS state and MFs at experimentally accessible temperatures T << E_{qp}. Here we show that the linear scaling of minigap with E_{qp} can fail in quasi-1D wires with multiple confinement bands when the applied Zeeman field is greater than or equal to about half of the confinement-induced bandgap. TS states in such wires have an approximate chiral symmetry supporting multiple near zero energy modes at each end leading to a minigap which can effectively vanish. We show that the problem of small minigap in such wires can be resolved by forcing the system to break the approximate chirality symmetry externally with a second Zeeman field. Although experimental signatures such as zero bias peak from the wire ends is suppressed by the second Zeeman field above a critical value, such a field is required in some important parameter regimes of quasi-1D wires to isolate the topological physics of end state MFs. We also discuss the crucial difference of our minigap calculations from the previously reported minigap results appropriate for idealized spinless p-wave superconductors and explain why the clustering of fermionic subgap states around the zero energy Majorana end state with increasing chemical potential seen in the latter system does not apply to the experimental TS states in spin-orbit coupled nanowires.