Competing Liquid and Crystal Phases in Bilayer Systems under High Magnetic Field

We investigate the nature of bilayer states in a high magnetic field as a function of the layer separation, filling factor, quantum well width, and electron density. Previous theoretical studies have investigated bilayer liquid states, but experiments have also found an insulating phase for a range of filling factors. We consider several types of liquid and crystal states at total filling factors 1/3, 2/5, 1/2, and 1/5, and determine the phase diagram as a function of the layer separation and density. We find that composite-fermion crystal phases are favored for appropriate parameters at 1/3, 2/5, and 1/5. These have either “binary graphene” or “correlated square” lattice structure. The theoretical phase diagram is compared with experiment.