Topological phases and surface flat bands in superconductors without inversion symmetry

TL;DR

This paper investigates topological phases in three-dimensional non-centrosymmetric superconductors with time-reversal symmetry, revealing flat surface bands and Majorana modes that have observable experimental signatures.

Contribution

It introduces a comprehensive analysis of topological invariants in non-centrosymmetric superconductors, identifying conditions for flat bands and Majorana modes.

Findings

Presence of zero-energy flat bands on surfaces due to topological invariants

Projection of bulk nodal lines determines flat band regions

Majorana surface modes protected by  topological invariant

Abstract

We examine different topological phases in three-dimensional non-centrosymmetric superconductors with time-reversal symmetry by using three different types of topological invariants. Due to the bulk boundary correspondence, a non-zero value of any of these topological numbers indicates the appearance of zero-energy Andreev surface states. We find that some of these boundary modes in nodal superconducting phases are dispersionless, i.e., they form a topologically protected flat band. The region where the zero-energy flat band appears in the surface Brillouin zone is determined by the projection of the nodal lines in the bulk onto the surface. These dispersionless Andreev surface bound states have many observable consequences, in particular, a zero-bias conductance peak in tunneling measurements. We also find that in the gapless phase there appear Majorana surface modes at time-reversal invariant momenta which are protected by a $\mathbb{Z}_2$ topological invariant.