Impurity effects in a two-dimensional topological superconductor: A link of Tc-robustness with a topological number

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Impurity effects are probes for revealing an unconventional property in superconductivity. We study effects of non-magnetic impurities, in a 2D topological superconductor with s-wave pairing, the Rashba spin-orbit coupling, and the Zeeman term. Using a self-consistent T-matrix approach, we calculate a phenomenological formula for the Thouless-Kohmoto-Nightingale-Nijs (TKNN) invariant in interacting systems, as well as density of states, with different magnetic fields. This quantity weakly depends on the magnetic field, when a spectral gap opens, whereas this changes drastically, when in-gap states occurs. Furthermore, in the latter case, we find that the Anderson's theorem (robustness of s-wave superconductivity against non-magnetic impurities) breaks down. We discuss the origin, from the viewpoints of both unconventional superconductivity and the TKNN invariant.