When Majoranas Delocalise
Krishnan Ganesh, CMTH Group
In recent years, there has been enormous excitement about the possibility of finding Majorana zero modes in topological superconductors. Most of this stems from the fact that they are a promising candidate for realising non-Abelian anyons – particles whose exchange statistics are non-commutative. Despite this, we still do not fully understand how one might exchange Majoranas in mesoscopic systems and reliably measure their exchange phases. The purpose of this talk will be two-fold: I will start with an introduction to Majorana physics in two-dimensional topological superconductors, with a particular emphasis on the interplay between bulk vortices and chiral edge modes. Following this, I will outline some recent ideas I have been thinking about to braid Majoranas using topological Josephson junctions, where their spatial position can be precisely controlled by applying phase biases. Time permitting, I will end the talk with some speculation about non-Abelian statistics in the deconfined state.