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

We consider the filling factor 5/2 fractional quantum Hall state of spin-polarized fermions in a dirty (mobility $μ_b \lt 10 m^2 V^{-1} s^{-1}$) bi-layer quantum well system.We show that the system undergoes a quantum phase transition from the effective two-component state to an effective single-component state, at fixed charge imbalance regulatory parameter $\Delta_{c}$ and constant layer separation, as the inter-layer tunneling strength $\Desta_\text{SAS}$ is increased. At finite and constant $\Delta_\text{SAS}$, a transition from the latter state to the former state is also possible upon increasing the parameter $\Delta_{c}$. 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 finite-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.