Self-consistent study of Abelian and non-Abelian order in a two-dimensional topological superconductor

We perform self-consistent studies of two-dimensional (2D) $s$-wave topological superconductivity (TSC) with Rashba spin-orbit coupling and Zeeman field by solving the Bogoliubov-de Gennes equations. In particular, we examine the effects of a nonmagnetic impurity in detail and show that the nature of the spin-polarised midgap bound state varies significantly depending on the material parameters. Most notably, a nonmagnetic impurity in a 2D $s$-wave topological superconductor can act like a magnetic impurity in a conventional $s$-wave superconductor, leading to phase transitions of the ground state as the impurity potential is varied. Furthermore, by solving for the spin-dependent Hartree potential self-consistently along with the superconducting order parameter, we demonstrate that topological charge density waves can coexist with TSC at half filling just as in a conventional $s$-wave superconductor.