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


We investigate the chemical potential μ and specific heat CV 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, CV(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.