Topological superconductivity in helical crystals

TL;DR

This paper explores topological superconductivity in helical crystals, analyzing surface states and zero-energy peaks associated with Andreev bound states across different surface orientations.

Contribution

It provides a detailed investigation of surface Andreev bound states and their topological origins in helical lattice superconductors, considering all irreducible representations.

Findings

Zero energy peaks appear in local density of states at specific surfaces.

Surface Andreev bound states are linked to nontrivial topological invariants.

Multiple irreducible representations exhibit these topological surface states.

Abstract

We study superconductivity and surface Andreev bound states in helical crystals. We consider the interlayer pairings along the helical hopping and investigate the surface local density of states on the (001) and zigzag surfaces for all the possible irreducible representations. There are three and four irreducible representations exhibiting the zero energy peaks in the local density of states at the (001) and zigzag surfaces of helical lattices, respectively. By calculating the one dimensional winging number, we show that these appearances of the zero energy peaks stem from the surface Andreev bound states.