Wigner transition temperature of a two-dimensional electron gas in a strong magnetic field

Within the Hartree-Fock approximation the transition temperature $T_c$ of a two-dimensional electron gas of density $n$ in a strong magnetic field $B$ is studied in the nondegenerate limit $\frac{n}{B}\to 0$. By means of an asymptotically correct calculation it is shown that the ansatz of a strongly anharmonic, unidirectional charge-density wave (CDW) for the condensed state leads, apart from weak logarithmic corrections, to the limiting form $T_c\sim n^{\frac{1}{2}}$. The ansatz of an essentially harmonic, though triangular symmetric CDW leads to much smaller limiting values $T_c\sim n{B}^{-\frac{1}{2}}$. This demonstrates the importance of the anharmonicity of the CDW or, equivalently, of the sharp localization of electronic wave functions in the nondegenerate limit.