Transition to an anharmonic charge-density wave of a two-dimensional electron gas in a strong magnetic field

The phase transition of a two-dimensional electron gas in a strong magnetic field to a charge-density-wave (CDW) state is considered within the Hartree-Fock approximation. A triangular CDW is found more favorable than a square CDW. With decreasing electron density $n$, higher harmonics are shown to become increasingly important, so that the linear density dependence of the (first-order) transition temperature $T_1$ ($T_1\sim n$), which is obtained if only the fundamental waves are considered, changes to a square-root dependence ($T_1\sim n^{\frac{1}{2}}$), which is familiar from the zero-magnetic-field limit. This transition is related by a simple argument to the onset of short-range order, and a phase diagram with two condensed phases is proposed which is consistent with the ideas of recent defect-melting theories.