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

摘要

We consider an isolated vortex in the two-dimensional proximity-inducedsuperconducting state formed at the interface of a three-dimensional strongtopological insulator (TI) and an s-wave superconductor (sSC). Priorcalculations of the bound states of this system famously revealed a zero-energystate 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-particleHamiltonian, inherited from the TI surface, affects the cross section forscattering Bogoliubov quasiparticles from the vortex. As in the case of anordinary superconductor, this is a two-channel problem with the vortex mixingparticle-like and hole-like excitations. And as in the ordinary case, thesame-channel differential cross section diverges in the forward direction dueto the Aharonov-Bohm effect, resulting in an infinite total cross section butfinite transport and skew cross sections. We calculate the transport and skewcross sections numerically, via a partial wave analysis, as a function of bothquasiparticle excitation energy and chemical potential. Novel effects emerge asparticle-like or hole-like excitations are tuned through the Dirac point.