Second-Order Bulk-Boundary Correspondence in Rotationally Symmetric Topological Superconductors from Stacked Dirac Hamiltonians

TL;DR

This paper establishes a bulk-boundary correspondence for rotationally symmetric second-order topological superconductors, linking Majorana boundary states to bulk invariants using stacked Dirac Hamiltonians.

Contribution

It introduces a novel approach using stacked Dirac Hamiltonians to relate bulk topological invariants to boundary Majorana states in rotationally symmetric superconductors.

Findings

Majorana boundary states depend on bulk rotational and weak invariants.

The presence of boundary states is influenced by the rotation center's position.

Numerical examples support the theoretical predictions.

Abstract

Two-dimensional second-order topological superconductors host zero-dimensional Majorana bound states at their boundaries. In this work, focusing on rotation-invariant crystalline topological superconductors, we establish a bulk-boundary correspondence linking the presence of such Majorana bound states to bulk topological invariants introduced by Benalcazar et al. We thus establish when a topological crystalline superconductor protected by rotational symmetry displays second-order topological superconductivity. Our approach is based on stacked Dirac Hamiltonians, using which we relate transitions between topological phases to the transformation properties between adjacent gapped boundaries. We find that in addition to the bulk rotational invariants, the presence of Majorana boundary bound states in a given geometry depends on the interplay between weak topological invariants and the location of the rotation center relative to the lattice. We provide numerical examples for our predictions and discuss possible extensions of our approach.