Scattering states of a vortex in the proximity-induced superconducting state at the interface of a topological insulator and ans-wave superconductor

Abstract

We consider an isolated vortex in the two-dimensional proximity-induced superconducting state formed at the interface of a three-dimensional strong topological insulator (TI) and an $s$-wave superconductor. Prior calculations of the bound states of this system famously revealed a zero-energy state that is its own conjugate, a Majorana fermion bound to the vortex core. We calculate, not the bound states, but the scattering states of this system, and ask how the spin-momentum-locked massless Dirac form of the single-particle Hamiltonian, inherited from the TI surface, affects the cross section for scattering Bogoliubov quasiparticles from the vortex. As in the case of an ordinary superconductor, this is a two-channel problem with the vortex mixing particlelike and holelike excitations. As in the ordinary case, the same-channel differential cross section diverges in the forward direction due to the Aharonov-Bohm effect, resulting in an infinite total cross section but finite transport and skew cross sections. We calculate the transport and skew cross sections numerically, via a partial wave analysis, as a function of both quasiparticle excitation energy and chemical potential. Novel effects emerge as particlelike or holelike excitations are tuned through the Dirac point.