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The specific heat capacity of a two-dimensional electron gas is derived fortwo types of the density of states, namely, the Dirac delta function spectrumand that based on a Gaussian function. For the first time, a closed formexpression of the specific heat for each case is obtained at half-filling. Whenthe chemical potential is temperature-independent, the temperature iscalculated at which the specific heat is a maximum. Here the effects of thebroadening of the Landau levels are distinguished from those of the differentfilling factors. In general, the results derived herein hold for anythermodynamic system having similar resonant states.

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