The Fractional Quantum Hall Effect and Liquid - Transitions in a Multiple-Quantum System.

The phases of a multiple-quantum-well system of layered two-dimensional electrons in a strong perpendicular magnetic field are studied. Solid phases are found at small fillings of the lowest Landau level which are the hexagonal-close-packed lattice at large interlayer separations and the body-centered-tetragonal lattice at small separations. A sequence of incompressible Laughlin-liquid-like states occurs at larger fillings. The energies and correlation functions of these states have been calculated by using Monte Carlo simulations. The quasiparticle and collective excitations of the liquid states are also discussed. The electric charge carried by a quasiparticle can have a contribution in one layer which is an irrational fraction of the electron charge. It should be possible to observe the transitions between different Laughlin-like phases experimentally. Transport and microwave experiments are particularly promising in this regard.