Bound states at impurities as a probe of topological superconductivity in nanowires

Spin-orbit coupled superconductors are interesting candidates for realizing topological and potentially nonAbelian states with Majorana fermions. We argue that time-reversal broken spin-orbit coupled superconductors generically can be characterized as having subgap states that are bound to localized nonmagnetic impurities. Such bound states, which are referred to as the Shiba states, can be detected as sharp resonances in the tunneling spectrum of the spin-orbit coupled superconductors. The Shiba state resonance can be tuned using a gate voltage or a magnetic field from being at the edge of the gap at zero magnetic fields to crossing zero energy when the Zeeman splitting is tuned into the topological superconducting regime. The zero-crossing signifies a fermion parity changing first-order quantum phase transition, which is characterized by a Pfaffian topological invariant. These zero crossings of the impurity level can be used to locally characterize the topological superconducting state in topological nanowires from tunneling experiments.