Phase diagram for topological superconductivity in topological insulator nanowires

A topological insulator nanowire can be used as a platform to produce one dimensional topological superconductivity in the presence of magnetic fields and the proximity effect from a nearby superconductor. In this work, we discuss the conditions under which this can happen by computing the topological invariant of the system from both a continuum Dirac fermion model and a lattice realization of a TI. We demonstrate that the presence of a vortex in the order parameter winding around the wire is essential to have a non-trivial invariant. In addition, we present a full phase diagram of the model as a function of chemical potential, flux and superconducting pairing, emphasizing that not all regions present a fully gapped superconducting state. Implications for transport in normal-superconductor junctions in this system will be discussed.