Wigner crystal states for the two-dimensional electron gas in a double quantum well system

TL;DR

This paper uses Hartree-Fock calculations to explore various Wigner crystal phases in a double quantum well system under strong magnetic fields, revealing phase transitions influenced by layer separation, interlayer hopping, and in-plane magnetic fields.

Contribution

It provides a detailed phase diagram of Wigner crystal states considering interlayer effects and magnetic fields, including the impact of anisotropy and a new experimental approach.

Findings

Ground state transitions from triangular to square lattices with increasing layer separation.

In-plane magnetic field induces a transition from commensurate to incommensurate states.

The anisotropy has negligible effect on the critical in-plane field at low filling fractions.

Abstract

Using the Hartree-Fock approximation, we calculate the energy of different Wigner crystal states for the two-dimensional electron gas of a double quantum well system in a strong magnetic field. Our calculation takes interlayer hopping as well as an in-plane magnetic field into consideration. The ground The ground state at small layer separations is a one-component triangular lattice Wigner state. As the layer separation is increased, the ground state first undergoes a transition to two stacked square 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 interlayer hopping is increased. An in-plane magnetic field induces another phase transition from a commensurate to a incommensurate state, similar to that of $\nu=1$ quantum Hall state observed recently. We calculate the critical value of the in-plane field of the transition and find that the anisotropy of the Wigner state, {\it i.e.,}, the relative orientation of the crystal and the in-plane magnetic field, has a negligible effect on the critical value for low filling fractions. The effect of this anisotropy on the low-lying phonon energy is discussed. A novel exerimental geometry is proposed in which the parallel magnetic field is used to enhance the orientational correlations in the ground state when the crystal is subject toa random potential.