# 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.

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*Proceedings of the Samahang Pisika ng Pilipinas*

**24**, SPP-2006-3G-01 (2006). URL: https://proceedings.spp-online.org/article/view/SPP-2006-3G-01.