Dislocation and Vortex Majorana Modes in Higher-Order Topological Superconductors

In this work, we show that an inversion-symmetric higher-order topological superconductor (HOTSC) features a new non-Abelian Majorana response to the insertion of either a lattice dislocation or a superconducting vortex. As a proof of concept, we consider a minimal lattice model of a doped topological insulator with an odd-parity pairing symmetry. A plethora of topological superconducting phases is found by tuning the chemical potential, including those with 1st-order, 2nd-order, and weak topologies. In particular, the 2nd-order topological phase features 0D Majorana zero modes at the ends of a dislocation/vortex line, while 1D helical Majorana modes will show up in the same defect of the 1st-order phase. Candidate materials and experimental consequences for the defect Majorana physics are also discussed.