Study on Green's function on TI surface

TL;DR

This paper develops a method to construct Green's functions on topological insulator surfaces, revealing how Majorana fermions influence local density of states and Josephson currents in superconductor-ferromagnet junctions.

Contribution

It introduces a Green's function construction on TI surfaces using McMillan's formalism and extends Josephson current formulas to include magnetization effects.

Findings

Majorana fermions enhance local density of states and odd-frequency pairing.

Extended Furusaki-Tsukada formula for Josephson current in S/F/S junctions.

Josephson current varies with magnetization direction and strength.

Abstract

In theory of superconducting junctions, Green's function has an important role to obtain Andreev bound states, local density of states and Josephson current in a systematic way. In this article, we show how to construct Green's function on the surface of topological insulator following McMillan's formalism where the energy spectrum of electrons obeys a linear dispersion. For a model of superconductor (S)/ferromagnet (F)/normal metal (N) junction, we show that the generation of Majorana Fermion gives rise to the enhanced local density of states and pair amplitude of odd-frequency pairing. We also derive an extended Furusaki-Tsukada's formula of d.c. Josephson current in S/F/S junctions. The obtained Josephson current depends on the direction and magnitude of the magnetization.