WIGNER-CRYSTAL STATES FOR THE 2-DIMENSIONAL ELECTRON-GAS IN A DOUBLE-QUANTUM-WELL SYSTEM

Using the Hartree-Fock approximation, we calculate the energy of diffe rent Wigner-crystal states for the two-dimensional electron gas of a d ouble-quantum-well system in a strong magnetic held. Our calculation t akes interlayer hopping, as well as an in-plane magnetic field into co nsideration. The ground state at small layer separations is a one-comp onent triangular lattice Wigner state. As the layer separation is incr eased, the ground state first undergoes a transition to two stacked sq uare lattices, and then undergoes another transition at an even larger layer separation to a two-component triangular lattice. The range of the layer separation at which the two-component square lattice occurs as the ground state shrinks, and eventually disappears, as the interla yer hopping is increased. An in-plane magnetic held induces another ph ase transition from a commensurate to an incommensurate state, similar to that of v = 1 quantum Hall state observed recently. We calculate t he critical value of the in-plane field of the transition and find tha t the anisotropy of the Wigner state, i.e., the relative orientation o f the crystal and the in-plane magnetic held, has a negligible effect on the critical value for low filling fractions. The effect of this an isotropy on the low-lying phonon energy is discussed. An experimental geometry is proposed in which the parallel magnetic held is used to en hance the orientational correlations in the ground state when the crys tal is subject to a random potential.