Symmetry-protected topological invariant and Majorana impurity states in time-reversal invariant superconductors

We address the question of whether individual nonmagnetic impurities can induce zero-energy states in time reversal invariant topological superconductors, and define a class of symmetries which guarantee the existence of such states for a specific value of the impurity strength [1]. These symmetries allow the definition of a position space topological $Z_2$ invariant, which is related to the standard bulk topological $Z_2$ invariant. Our general results are applied to the time reversal invariant $p$-wave phase of the doped Kitaev-Heisenberg model [2], where we demonstrate how a lattice of impurities can drive a topologically trivial system into the non-trivial phase. Finally, signatures of impurity states in the spin-susceptibility are described.\\[4pt] [1] L.~Kimme, T.~Hyart, and B.~Rosenow, arXiv:1308.2496, (2013).\\[0pt] [2] T.~Hyart, A.R.~Wright, G.~Khaliullin, and B.~Rosenow, Phys. Rev. B 85, 140510(R) (2012).