The intrinsic features of the specific heat at half-filled Landau levels of two-dimensional electron systems

TL;DR

This paper derives closed-form expressions for the specific heat of a two-dimensional electron gas at half-filled Landau levels, analyzing effects of Landau level broadening and filling factors, with implications for similar resonant systems.

Contribution

It provides the first closed-form expressions for the specific heat at half-filling in two types of density of states, considering broadening effects and temperature-independent chemical potential.

Findings

Maximum specific heat occurs at a calculable temperature.

Broadening of Landau levels influences specific heat behavior.

Results applicable to other thermodynamic systems with resonant states.

Abstract

The specific heat capacity of a two-dimensional electron gas is derived for two types of the density of states, namely, the Dirac delta function spectrum and that based on a Gaussian function. For the first time, a closed form expression of the specific heat for each case is obtained at half-filling. When the chemical potential is temperature-independent, the temperature is calculated at which the specific heat is a maximum. Here the effects of the broadening of the Landau levels are distinguished from those of the different filling factors. In general, the results derived herein hold for any thermodynamic system having similar resonant states.