Finite Temperature Behavior of the $\nu=1$ Quantum Hall Effect in Bilayer Electron Systems

TL;DR

This paper uses effective field theory and renormalization group methods to analyze the temperature-dependent phase transition in $ u=1$ bilayer quantum Hall systems, explaining experimental observations.

Contribution

It provides a theoretical framework for understanding the crossover from quantum Hall to compressible states in bilayer systems at finite temperature.

Findings

Identifies a crossover temperature between quantum Hall and compressible states.

Shows the crossover temperature's dependence on electron density aligns with experiments.

Offers an estimate for the temperature at which the phase transition occurs.

Abstract

An effective field theoretic description of $\nu=1$ bilayer electron systems stabilized by Coulomb repulsion in a single wide quantum well is examined using renormalization group techniques. The system is found to undergo a crossover from a low temperature strongly correlated quantum Hall state to a high temperature compressible state. This picture is used to account for the recent experimental observation of an anomalous transition in bilayer electron systems (T. S. Lay, {\em et al.} Phys. Rev. B {\bf 50}, 17725 (1994)). An estimate for the crossover temperature is provided, and it is shown that its dependence on electron density is in reasonable agreement with i the experiment.