Ideal two-dimensional electron gas in a magnetic field and at non-zero temperatures : an alternative approach

Abstract

A new exact expression is derived for the free energy of an ideal two-dimensional electron gas (2DEG) in a uniform magnetic field and at low, but finite, temperatures. The approach eliminates a 2D-peculiarity that neither the weak nor the strong magnetic field limit can be easily taken in the result derived from the standard Sondheimer-Wilson treatment. In the strong magnetic field limit, the result reduces to an existing one, for which a misunderstanding needs to be clarified. In the weak field limit, it agrees with a result obtainable through Euler's summation formula. The conditions are discussed under which the nondegenerate situation may occur.