Bulk-Vortex Correspondence of Higher-Order Topological Superconductors

TL;DR

This paper establishes a universal bulk-vortex correspondence in higher-order topological superconductors, showing that vortices trap protected Majorana modes, providing a new way to experimentally detect higher-order topology.

Contribution

It introduces a model-independent framework linking vortex Majorana modes to higher-order topology in 2D superconductors, confirmed by an exactly solvable model.

Findings

Vortices trap pairs of Majorana bound states with specific angular momenta.

A systematic, model-independent derivation of vortex-bound states in higher-order topological superconductors.

Confirmation of the theory through an exactly solvable model.

Abstract

Vortices in chiral topological superconductors are known for trapping Majorana zero modes as a signature response to their bulk-state topologies. In this work, we establish a similar bulk-vortex correspondence for two-dimensional $C_n$-protected class D higher-order topological superconductors, in which a quantum vortex will universally trap a pair of $C_n$-protected Majorana bound states with $\hat{z}$-directional angular momenta $J_z=0$ and $J_z=n/2$, respectively. This intriguing one-to-one mapping between anomalous vortex modes and higher-order topology can be systematically derived through a model-independent patch construction approach. As a proof of concept, we present an exactly solvable model to confirm the proposed vortex Majorana modes. Our theory establishes vortices as an unprecedented experimental measure of higher-order topology in superconductors.