Quasi-Particle Localization by Disorder in ν = 5/2 Fractional Quantum Hall State and Its Potential Application

Abstract

We consider the lling factor 5/2 fractional quantum Hall state of spin-polarized fermions in a dirty (mobility µ b < 10 m 2 V −1 s −1 ) bi-layer quantum well system.We show that the system undergoes a quantum phase transition from the eective two-component state to an eective single-component state, at xed charge imbalance regulatory parameter ∆c and constant layer separation, as the inter-layer tunneling strength ∆SAS is increased. At nite and constant ∆SAS, a transition from the latter state to the former state is also possible upon increasing the parameter ∆c. We identify the order parameter to describe quantum phase transition as a pseudo-spin component and calculate this with the aid of the Matsubara propagators in the nite-temperature formalism. Our treatment is able to show that, at low temperature(< 0.1 K) and low value of charge imbalance regulatory parameter, there is a competition between the disorder and the inter-layer tunneling strength in the sample. The competition leads to the quasi-particle localization at low tunneling strength.