Quantum Hall effect in single wide quantum wells

TL;DR

This paper investigates quantum Hall states in wide quantum wells, revealing a phase transition from an incompressible to a compressible state driven by electron density, with implications for fractional quantum Hall states.

Contribution

It provides numerical and theoretical analysis of phase transitions in wide quantum wells, including the effects of magnetic field, well width, and electron density on quantum Hall states.

Findings

Identified a critical electron density for phase transition.

Showed the renormalization of tunneling and interlayer separation by magnetic field.

Demonstrated agreement between many-body and density functional calculations.

Abstract

We study the quantum Hall states in the lowest Landau level for a single wide quantum well. Due to a separation of charges to opposite sides of the well, a single wide well can be modelled as an effective two level system. We provide numerical evidence of the existence of a phase transition from an incompressible to a compressible state as the electron density is increased for specific well width. Our numerical results show a critical electron density which depends on well width, beyond which a transition incompressible double layer quantum Hall state to a mono-layer compressible state occurs. We also calculate the related phase boundary corresponding to destruction of the collective mode energy gap. We show that the effective tunneling term and the interlayer separation are both renormalised by the strong magnetic field. We also exploite the local density functional techniques in the presence of strong magnetic field at $\nu=1$ to calculate renormalized $\Delta_{SAS}$. The numerical results shows good agreement between many-body calculations and local density functional techniques in the presence of a strong magnetic field at $\nu=1$. we also discuss implications of this work on the $\nu=1/2$ incompressible state observed in SWQW.