The thermodynamics of a charged fermion layer at high r_s values

We report the measurement of the chemical potential of a two-dimensional hole layer in wide temperature and density ranges. Due to their heavy mass, the holes are in a regime where the ratio of Coulomb to Fermi energies rs is very high, thus facilitating the first detailed study of the full temperature-dependent crossover from the strongly interacting degenerate regime to the classical ideal gas limit. The measured low-temperature chemical potential and inverse compressibility are negative and uninfluenced by temperature. At T≈17 K they simultaneously and abruptly become temperature-dependent for all carrier concentrations. As the temperature is further raised, the inverse compressibility becomes less negative and reverses sign. An ideal classical gas behavior is attained only at temperatures of the order of the interaction energy, more than an order of magnitude larger than the Fermi energy.