CDW instability of electron gas in a strong magnetic field

It is shown that within the Hartree-Fock approximation the electron gas in the quantum limit of a strong magnetic field has an instability as the temperature is lowered toward the charge density wave state with an wave-vector which has finite components in the directions not only parallel but also perpendicular to the field. The critical temperature, T_c, is estimated under the assumption of T_c??_F?ω_c, where ?_F and ω_c are the Fermi energy of the non-interacting system and the cyclotron frequency respectively.