Electronic transport in an array of quasiparticles in theν=5∕2non-Abelian quantum Hall state

Abstract

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