General theory of robustness against disorder in multi-band superconductors

We investigate the influence of general forms of disorder on the robustness of superconductivity in multiband materials. Specifically, we consider a general two-band system where the bands arise from an orbital degree of freedom of the electrons. Within the Born approximation, we show that the interplay of the spin-orbital structure of the normal-state Hamiltonian, disorder scattering, and superconducting pairing potentials can lead to significant deviations from the expected robustness of the superconductivity. This can be conveniently formulated in terms of the so-called "superconducting fitness". In particular, we verify a key role for unconventional $s$-wave states, permitted by the spin-orbital structure and which may pair electrons that are not time-reversed partners. To exemplify the role of Fermi surface topology and spin-orbital texture, we apply our formalism to the candidate topological superconductor Cu$_x$Bi$_2$Se$_3$, for which only a single band crosses the Fermi energy, as well as models of the iron pnictides, which possess multiple Fermi pockets.