Thermodynamic properties of a two dimensional electron gas in the fractional quantum Hall regime

Abstract

We investigate the chemical potential μ and specific heat C_V of a two-dimensional electron gas at temperatures T < 1 K subject to high magnetic fields B that correspond to filling factors ν < 1. We found out that at ν = 1/2 , the chemical potential is pinned at ħω_c/2 which is equal to the energy of the first Landau level. The μ(T) increases when ν > 1/2 and decreases when ν < 1/2 . This behavior is dictated by the change in the number of states available to the electrons. We also found out that μ(B) converged at ħω_c/2 and this trend has a negligible T-dependence. When this behavior of the chemical potential was used in calculating the specific heat at the fractional quantum Hall filling factors, C_V(T) exhibited a humpy behavior as compared to its smoothly increasing trend at the integral quantum Hall regime. This trend is a direct consequence of the discontinuities in the chemical potential.