Study on Green's function on topological insulator surface

Bo Lu; Yukio Tanaka

doi:10.1098/rsta.2015.0246

Study on Green's function on topological insulator surface

Philos Trans A Math Phys Eng Sci. 2018 Aug 6;376(2125):20150246. doi: 10.1098/rsta.2015.0246.

Authors

Bo Lu¹, Yukio Tanaka²

Affiliations

¹ Department of Applied Physics, CREST, Japan Science and Technology Corporation (JST), Nagoya University, Nagoya 464-8603, Japan dr.lv.bo@gmail.com.
² Department of Applied Physics, CREST, Japan Science and Technology Corporation (JST), Nagoya University, Nagoya 464-8603, Japan.

Abstract

In the theory of superconducting junctions, Green's function has an important role for obtaining 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 a topological insulator following McMillan's formalism where the energy spectrum of electrons obeys a linear dispersion. For a model of a superconductor (S)/ferromagnet (F)/normal metal (N) junction, we show that the generation of a 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 DC Josephson current in S/F/S junctions. The obtained Josephson current depends on the direction and magnitude of the magnetization.This article is part of the theme issue 'Andreev bound states'.

Keywords: Josephson effect; McMillan’s Green’s function; odd-frequency pairing; topological Insulator.