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

16 pages, 7 figures; modified title, improved figures, as published in PRB

References in corpus (10)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Topological Insulators with Inversion Symmetry
• Discovery (theoretical prediction and experimental observation) of a large-gap topological-insulator class with spin-polarized single-Dirac-cone on the surface
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Andreev reflection and Klein tunneling in graphene
• Three dimensional topological invariants for time reversal invariant Hamiltonians and the three dimensional quantum spin Hall effect
• Specular Andreev reflection in graphene
• Tunneling spectrum of a pinned vortex with a robust Majorana state

Cited by in corpus (1)

• Bound fermion states in pinned vortices in the surface states of a superconducting topological insulator: The Majorana bound state