Superconductive proximity in a Topological Insulator slab and excitations bound to an axial vortex

TL;DR

This paper investigates the proximity effect in a topological insulator slab with superconducting contacts, analyzing Majorana and Andreev bound states under different pairing symmetries and vortex configurations.

Contribution

It provides a detailed derivation of the quantum field for midgap fermions in a topological insulator with proximity-induced superconductivity, highlighting differences between s-wave and odd-parity pairings.

Findings

Majorana bound states appear with s-wave proximity.

Odd-parity pairing leads to charged surface Andreev bound states.

Extended vortex states depend on bulk band symmetry.

Abstract

We consider the proximity effect in a Topological Insulator sandwiched between two conventional superconductors, by comparing s-wave spin singlet superconducting pairing correlations and odd-parity triplet pairing correlations with zero spin component orthogonal to the slab ("polar " phase). A superconducting gap opens in the Dirac dispersion of the surface states existing at the interfaces. An axial vortex is included, piercing the slab along the normal to the interfaces with the superconductors. It is known that, when proximity is s-wave, quasiparticles in the gap are Majorana Bound States, localized at opposite interfaces. We report the full expression for the quantum field associated to the midgap neutral fermions, as derived in the two-orbital band model for the TI. When proximity involves odd-parity pairing, midgap modes are charged Surface Andreev Bound States, and they originate from interfacial circular states of definite chirality, centered at the vortex singularity and decaying in the TI film with oscillations. When the chemical potential is moved away from midgap, extended states along the vortex axis are also allowed. Their orbital structure depends on the symmetry of the bulk band from where the quasiparticle level splits off.