Discernable signature of QPT in a bilayer-quantum-well system at the filling fraction {\nu} = 5/2 in the low temperature range (1K-100 K)

TL;DR

This paper investigates a quantum phase transition in a bilayer quantum well system at filling fraction 5/2, revealing a transition from a two-component to a single-component state driven by inter-layer tunneling strength, observable up to 100 K.

Contribution

It demonstrates the existence of a zero-order quantum phase transition in a bilayer quantum Hall system at finite temperature, characterized by a pseudo-spin order parameter.

Findings

Identification of a quantum phase transition at finite temperature.

Transition from two-component to single-component state with increasing ILTS.

Observable signatures of the QPT up to 100 K.

Abstract

We consider the spin polarized fermions for the filling fraction 5/2 in a bi-layer quantum well system. Since the kinetic energy of the system in fractional quantum Hall states is totally quenched, the Hamiltonian describing the system comprises of the electron correlation and tunneling terms. The correlations are captured by the 'so-called' Haldane pseudo-potentials. We employ the finite-temperature formalism involving Matsubara propagators to deal with this Hamiltonian. We show that the system undergoes a zero-order quantum phase transition (QPT), at fixed charge imbalance regulatory parameter (CIRP) and constant layer separation as the inter-layer tunneling strength (ILTS) is increased, from the effective two-component state (two independent layers) to an effective single-component state (practically a single layer). At finite and constant ILTS, a transition from the latter state to the former state is also possible upon increasing the CIR parameter. We identify the order parameter to describe this QPT as a pseudo-spin component (analogous to the z-component of the single spin-1/2 operator S) and calculate the order parameter with the aid of the Matsubara propagators. The clear finger-print of this QPT is obtained up to temperature equal to 100 K.