Analytical Fermi energy for broadened Landau levels of 2DEG under a perpendicular strong magnetic field

Abstract

An analytical form of the Fermi energy is derived for broadened Landau levels (LLs) of the two-dimensional electron gas (2DEG) under a perpendicular strong magnetic field. A Gaussian density of states with the broadening parameter Γ is used to derive the analytical form under the assumption of asymptotically non-overlapping states between two consecutive Landau levels, i.e. Γ/ħωc → 0. It is shown that the smoothening of the Fermi energy around the neighborhood for fully filled Landau levels is due to the linear dependence of Γ and its factor with the inverse error function. The validity of the analytical form shows a threshold up to Γ/ħωc ∼ 0.23.