Electronic transport in an array of quasi-particles in the nu=5/2 non-abelian quantum Hall state

TL;DR

This paper investigates how tunneling between Majorana zero modes in the $ u=5/2$ quantum Hall state affects electronic transport, revealing a mechanism for dissipative conductivity at low frequencies and its dependence on deviation from the filling factor.

Contribution

It introduces a model for dissipative transport due to vortex core tunneling in the non-Abelian $ u=5/2$ quantum Hall state, with detailed ${f q},oldsymbol{ extomega}$ dependence.

Findings

Dissipative conductivity arises at frequencies below the gap.

Transport contributions depend exponentially on $| u-5/2|^{-1/2}$.

The study provides a quantitative framework for electronic response in this state.

Abstract

The Moore-Read Pfaffian $\nu=5/2$ quantum Hall state is a p-wave super-conductor of composite fermions. Small deviations from $\nu=5/2$ result in the formation of an array of vortices within this super-conductor, each supporting a Majorana zero mode near its core. Here we consider how tunneling between these cores is reflected in the electronic response to an electric field of non-zero wave vector $\bf q$ and frequency $\omega$. We find a mechanism for dissipative transport at frequencies below the $\nu=5/2$ gap, and calculate the ${\bf q},\omega$ dependence of the dissipative conductivity. The contributions we find depend exponentially on $|\nu-5/2|^{-1/2}$.