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

### Abstract

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.