Corner states in a second-order topological superconductor and their braiding

We model a second-order topological phase realized in a thin-film p-wave superconductor under the influence of an in-plane Zeeman field and proximity-induced spin-singlet pairing. This system exhibits two topologically-protected Majorana states localized at the corners of a square-shaped sample. By tuning certain Hamiltonian parameters, the centers of the two excitations can be shifted to various corners, while their energy is zero as long as particle-hole symmetry (PHS) is conserved. Within this degenerate ground-state manifold, we show there exists a closed path corresponding to the adiabatic braiding of the corner states. In one cycle, each Majorana accumulates a statistical phase π, which confirms their fractional statistics. This property, alongside the PHS-ensured Majorana operator algebra, suggests the proposed two-dimensional system might be a step toward topologically-protected non-Abelian braiding. The concept of a possible experimental realization of the proposed superconductor is presented.