Thermodynamics of a Charged Fermion Layer at HighrsValues

The chemical potential $\mu$ of a hole layer is mapped as a function of temperature and density $p$. We present the first investigation of the crossover from the strongly interacting degenerate regime to the classical ideal gas limit. The low temperature inverse compressibility, ${\kappa }^{-1\mathrm{}}\equiv p^2\partial \mu /\partial p$, is negative and temperature independent. At $T\approx 17\mathrm{K}$ temperature dependence commences abruptly: ${\kappa }^{-1\mathrm{}}$ turns less negative with rising $T$ and eventually reverses sign. An ideal classical gas is attained at temperatures comparable to the interaction energy, more than an order of magnitude larger than the Fermi energy.