Majoranas in topological josephson junctions
File(s)
Author(s)
Ganesh, Krishnan
Type
Thesis
Abstract
This thesis studies the use of topological Josephson junctions to manipulate, braid and measure properties of Majorana zero modes (MZMs) bound to Josephson vortices. We focus on two similar, but topologically distinct platforms. First, we consider planar Josephson junctions formed out of a two-dimensional electron gas with strong Rashba spin-orbit coupling, contacted by two s-wave superconducting electrodes and exposed to an in-plane Zeeman field. In such devices, the Andreev bound states are driven into a topologically non-trivial configuration, for particular values of the in-plane Zeeman coupling and Josephson phase difference. Further application of an out-of-plane magnetic flux can nucleate an integer number of Josephson vortices in the junction, each localising 2 MZMs. We demonstrate how the in-plane Zeeman field can be used to experimentally control the separation between the MZMs, thus serving as a possible fusion method, and how this process results in a parity-dependent magnetic moment aligned along the junction axis. Our findings are accompanied by a method to probe the spin characteristics of the fusing MZMs through local spin-resolved Andreev conductance measurements at the junction endpoints. For the second platform, we analyse a similar system where the underlying two-dimensional electron gas is replaced by a two-dimensional topological insulator. With this simple difference, the superconductors may be driven into a topological state that supports chiral Majorana edge modes flowing around the device perimeter. We investigate the interesting possibility of using these chiral edge states to exchange MZMs bound to Josephson vortices through phase biasing alone. Our study proceeds by describing the symmetries that may quantise the value of the exchange phase and numerically evaluates the associated Zak phase in a fixed parity sector. Furthermore, we discuss a possible method to probe this exchange phase through charging effects, before discussing the limitations and experimental challenges associated with observing this phenomenon.
Version
Open Access
Date Issued
2025-08-26
Date Awarded
2026-04-01
Copyright Statement
Attribution-NonCommercial 4.0 International Licence (CC BY-NC)
License URL
Advisor
Lee, Derek
Sponsor
Engineering and Physical Sciences Research Council
Grant Number
EP/T51780X/1
Publisher Department
Department of Physics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)