Interplay of topological charge density waves and superconductivity in a two-dimensional topological superconductor

We perform microscopic mean-field studies of topological order in a two-dimensional $s$-wave topological superconductor with Rashba spin-orbit coupling and Zeeman field in the Bogoliubov-de Gennes formalism. By solving for the spin-dependent Hartree potential self-consistently along with the superconducting order parameter, we show that topological charge density waves (TCDW) can coexist with topological superconductivity (TSC) at half filling just as in a conventional $s$-wave superconductor. Furthermore, we examine the effects of a nonmagnetic impurity, which tends to create spin-polarised midgap excitation and pin the phase of charge density modulations, on possible interplay of TCDW and TSC.