Fingerprint 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 quantum phase transitions in a bilayer quantum well system at filling fraction 5/2, revealing temperature-dependent fingerprints of these transitions through theoretical analysis of pseudo-spin order parameters.

Contribution

It introduces a finite-temperature formalism to analyze quantum phase transitions in bilayer quantum Hall systems, highlighting the transition from two-component to single-component states with temperature effects.

Findings

Identification of a zero-order quantum phase transition driven by inter-layer tunneling.

Observation of the transition fingerprint up to 100 K.

Demonstration of the transition's dependence on charge imbalance and tunneling strength.

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 (FQHS) 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(HPP). 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(CIR) parameter and constant layer separation as the inter-layer tunneling (ILT)strength 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 ILT strength, a transition from the latter state to the former state is also possible upon increasing CIR parameter. We identify the order parameter to describe this QPT as a pseudo-spin component 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.