Josephson and proximity effects on the surface of a topological insulator

TL;DR

This paper analyzes Josephson and proximity effects on a topological insulator surface with superconductors and a ferromagnet, providing analytical formulas and exploring their dependence on various parameters.

Contribution

It offers the first analytical expressions for Josephson current and proximity-induced pairing, including odd-frequency triplet components, on a topological insulator surface.

Findings

Josephson current depends on junction length, temperature, chemical potential, and magnetization.

Proximity effect induces even and odd frequency triplet pairings.

Analytical formulas reveal complex pairing symmetries on the topological insulator surface.

Abstract

We investigate Josephson and proximity effects on the surface of a topological insulator on which superconductors and a ferromagnet are deposited. The superconducting regions are described by the conventional BCS Hamiltonian, rather than the superconducting Dirac Hamiltonian. Junction interfaces are assumed to be dirty. We obtain analytical expressions of the Josephson current and the proximity-induced anomalous Green's function on the topological insulator. The dependence of the Josephson effect on the junction length, the temperature, the chemical potential and the magnetization is discussed. It is also shown that the proximity-induced pairing on the surface of a topological insulator includes even and odd frequency triplet pairings as well as a conventional s-wave one.