# Theory of Josephson Current on a Magnetically Doped Topological Insulator

## TL;DR

This paper develops a theoretical framework to analyze how the Josephson current and local density of states in magnetically doped topological insulators change across topological and metal-insulator phase transitions, highlighting the emergence of chiral Majorana modes.

## Contribution

It provides an analytical calculation of the Josephson current and density of states considering topological phase transitions in magnetically doped topological insulators.

## Key findings

- Josephson current magnitude increases when surface states become metallic.
- Temperature dependence of Josephson current changes drastically at the topological transition.
- Chiral Majorana modes influence the superconducting properties at the phase transition.

## Abstract

Proximity induced superconducting states in the surface of magnetically doped topological insulators can host chiral Majorana modes. We consider a Josephson junction in that system with changing the chemical potential, which drives a topological phase transition in the induced superconducting states as well as a metal-insulator transition in the surface states. The local density of states and the Josephson current are analytically calculated by McMillan's Green's function method in terms of the Andreev reflection coefficient. We show that although the magnitude of the Josephson current is greatly enhanced when the surface state changes from insulating to metallic, its temperature dependence drastically changes at the topological phase transition point, reflecting the appearance of the chiral Majorana modes