Majorana Fermions and Disclinations in Topological Crystalline Superconductors

TL;DR

This paper establishes a topological criterion for Majorana zero-modes at disclinations in 4-fold symmetric topological crystalline superconductors, revealing new bound states including corner Majoranas in trivial phases.

Contribution

It introduces a complete topological classification of TCS using invariants and derives a Z_2-index for Majorana modes at disclinations, including weakly protected corner states.

Findings

Topological classification of TCS with Chern and rotation invariants

A Z_2-index predicting Majorana zero-modes at disclinations

Discovery of corner Majoranas in trivial phases

Abstract

We prove a topological criterion for the existence of zero-energy Majorana bound-state on a disclination, a rotation symmetry breaking point defect, in 4-fold symmetric topological crystalline superconductors (TCS). We first establish a complete topological classification of TCS using the Chern invariant and three integral rotation invariants. By analytically and numerically studying disclinations, we algebraically deduce a Z_2-index that identifies the parity of the number of Majorana zero-modes at a disclination. Surprisingly, we also find weakly-protected Majorana fermions bound at the corners of superconductors with trivial Chern and weak invariants.