Bulk-Vortex Correspondence of Higher-Order Topological Superconductors

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. 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 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.