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

TL;DR

This paper analyzes how the unique spin-momentum locking of topological insulator surface states influences scattering processes of quasiparticles around a vortex in a proximity-induced superconductor, revealing novel effects near the Dirac point.

Contribution

It calculates the scattering states and cross sections of quasiparticles in a topological insulator-superconductor vortex system, highlighting effects of Dirac surface states on scattering behavior.

Findings

Forward scattering divergence due to Aharonov-Bohm effect

Transport and skew cross sections are finite and numerically computed

Novel effects occur as excitations are tuned through the Dirac point

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 (sSC). 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 particle-like and hole-like excitations. And 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 particle-like or hole-like excitations are tuned through the Dirac point.