Theoretical study on Majorana Fermions in Josephson junctions on a topological insulator

Abstract

Majorana Fermions in topological superconductor attracted may interests due to its possibility as a platform for fault tolerant quantum operation using braiding, and hence the detection and realization of topological superconductivity and Majorana Fermion has been important issues. One set up for realization of topological superconductivity is a Josephson junction made by inducing trivial superconducting pairing to topological surface mode of 3-dimensional topological insulator. Due to its controllability of properties and behaviors using global superconductor phase difference and magnetic field, the Majorana Fermions inside this device are expected as elements of more manipulative realization of braiding operation compared to other devices. In this thesis I will theoretically study the physics of Majorana Fermions inside the 3D topological insulator planar Josephson junction and its effect on Josephson current. I will also analyze how the behaviors and signals of the Majorana Fermions are affect by external channels originated from the region uncovered by superconductor, which is not well discussed in previous researches. Finally, I will discuss the additional difficulties of detecting signatures of Majorana fermions caused by this effect.