Ideal Two‐Dimensional Electron Gas in a Magnetic Field and at Non‐Zero Temperatures. An Alternative Approach

Abstract

AbstractA 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.