Compressibility of the two-dimensional electron gas: Measurements of the zero-field exchange energy and fractional quantum Hall gap

A quantitative study of the compressibility of the two-dimensional electron gas in GaAs heterostrutures is reported. Using a recently developed capacitive technique that avoids the large offset signals characteristic of conventional methods, high-precision compressibility data at both zero and high magnetic field has been obtained. The curious negative sign of the compressibility in certain regimes is shown to be a consequence of electron-electron interactions. Detailed numerical calculations show that the zero-field data are fully consistent with the known exchange energy, provided the finite thickness of the electron gas is properly included. At high magnetic fields, in the extreme quantum limit, the integrated compressibility signal is used to obtain a quantitative measure of the chemical potential discontinuity associated with the ν=1/3 fractional quantum Hall effect. Comparison with a theoretical model which includes quasiparticle interactions has allowed a determination of the inhomogeneous broadening due to density fluctuations and has provided evidence of a second, apparently distinct, source of disorder. While the origin of this disorder is not fully understood, the data are consistent with simple lifetime broadening of the quasiparticle states.