Quantum Hall effect in single wide quantum wells

We study the quantum Hall states in the lowest Landau level for a single wide quantum well (SWQW). Due to a separation of charges to opposite sides of the well, a single wide well can be modeled as an effective two layer system. We provide numerical evidence of the existence of a phase transition from an incompressible double layer quantum Hall state to a compressible monolayer state at a critical electron density that depends on well width. We also calculate the related phase boundary corresponding to the destruction of the collective mode energy gap. We show that the effective tunneling term ${\mathrm{\Delta }}_{\mathrm{SAS}}$ and the interlayer separation d are both renormalized by a strong magnetic field. We also make use of the local density approximation (LDA) in the presence of a strong magnetic field at filling factor ν=1 to calculate the renormalized tunneling term. Our results show good agreement between the many-body calculations and the LDA in the presence of a strong magnetic field at ν=1. Finally, we discuss implications of this work on the ν=1/2 incompressible state observed in the SWQW.