Multiband s-wave topological superconductors: role of dimensionality and magnetic field response

TL;DR

This paper explores the properties of two-band s-wave topological superconductors across different dimensions, analyzing the effects of magnetic fields and symmetry breaking on Majorana modes and topological phases.

Contribution

It extends the understanding of topological invariants and Majorana modes in multi-dimensional settings and under symmetry-breaking perturbations.

Findings

Topological phases support odd Kramers' pairs of Majorana modes on boundaries.

Breaking time-reversal symmetry modifies topological invariants and affects Majorana mode robustness.

Zeeman field can induce a transition from helical to chiral superconducting phases.

Abstract

We further investigate a class of time-reversal-invariant two-band s-wave topological superconductors introduced in Phys. Rev. Lett. 108, 036803 (2012). We show how, in the presence of time-reversal symmetry, Z_2 invariants that distinguish between trivial and non-trivial quantum phases can be constructed by considering only one of the Kramers' sectors in which the Hamiltonian decouples into. We find that the main features identified in our original 2D setting remain qualitatively unchanged in 1D and 3D, with non-trivial topological superconducting phases supporting an odd number of Kramers' pairs of helical Majorana modes on each boundary, as long as the required $\pi$ phase difference between gaps is maintained. We also analyze the consequences of time-reversal symmetry-breaking either due to the presence of an applied or impurity magnetic field or to a deviation from the intended phase matching between the superconducting gaps. We demonstrate how the relevant notion of topological invariance must be modified when time-reversal symmetry is broken, and how both the persistence of gapless Majorana modes and their robustness properties depend in general upon the way in which the original Hamiltonian is perturbed. Interestingly, a topological quantum phase transition between helical and chiral superconducting phases can be induced by suitably tuning a Zeeman field in conjunction with a phase mismatch between the gaps. Recent experiments in doped semiconducting crystals, of potential relevance to the proposed model, and possible candidate material realizations in superconductors with $s_\pm$ pairing symmetry are discussed.