Charge response of the Majorana toric code

TL;DR

This paper analyzes the charge response of a Majorana toric code system at phase transitions, calculating universal conductivities and superconducting density changes, and suggests the presence of an additional tricritical point.

Contribution

It applies a Landau field theory to study charge responses at phase transitions in the Majorana toric code, including calculations of universal conductivity and phase diagram features.

Findings

Universal conductivity at 3D-XY transitions calculated

Change in superconducting density at Ising transition determined

Evidence for an additional tricritical point in the phase diagram

Abstract

At zero temperature, a two dimensional lattice of Majorana zero modes on mesoscopic superconducting islands has a topologically ordered toric code phase. Recently, a Landau field theory has been proposed for the system that captures its different phases and the associated phase-transitions. It was shown that with the increase of Josephson tunneling between the islands, a continuous symmetry-breaking 3D-XY transition gets transformed into a discrete symmetry-breaking 3D-Ising transition through a couple of tricritical points and first order transitions. Using the proposed field theory, we analyze the charge-response of the system at the different continuous phase-transitions. We calculate the universal conductivity at the 3D-XY transitions and the change in the superconducting density at the Ising transition using 1/N expansion. Furthermore, by computing a one-loop correction to the field theory, we show that an additional tricritical point is likely to be present in the phase-diagram. Finally, we provide a mean-field calculation that supports the earlier proposed field theory.