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Non-fragile superconductivity with nodes in the superconducting topological insulator CuxBi2Se3: Zeeman orbital field and non-magnetic impurities

We study the robustness against non-magnetic impurities in the topological superconductor with point nodes, focusing on an effective model of Cu$_{x}$Bi$_{2}$Se$_{3}$. We find that the topological superconductivity with point-nodes is not fragile against non-magnetic impurities, although the superconductivity with nodes in past studies is usually fragile. Exchanging the role of spin with the one of orbital, and vice versa, we find that in the "dual" space the topological superconductor with point-nodes is regarded as the intra-orbital spin-singlet $s$-wave one. From the viewpoint of the dual space, we deduce that the point-node state is not fragile against non-magnetic impurity, when the orbital imbalance in the normal states is small. Since the spin imbalance is induced by the Zeeman magnetic field, we shall name this key quantity for the impurity effects Zeeman "orbital" field. The numerical calculations support that the deduction is correct. If the Zeeman orbital field is small, the topological superconductivity is not fragile in dirty materials, even with nodes. Thus, the topological superconductors can not be simply regarded as one of the conventional unconventional superconductors.