COMPRESSIBILITY OF THE 2-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 ele ctron gas in GaAs heterostrutures is reported. Using a recently develo ped capacitive technique that avoids the large offset signals characte ristic of conventional methods, high-precision compressibility data at both zero and high magnetic field has been obtained. The curious nega tive sign of the compressibility in certain regimes is shown to be a c onsequence of electron-electron interactions. Detailed numerical calcu lations show that the zero-field data are fully consistent with the kn own 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 quan titative measure of the chemical potential discontinuity associated wi th the nu = 1/3 fractional quantum Hall effect. Comparison with a theo retical model which includes quasiparticle interactions has allowed a determination of the inhomogeneous broadening due to density fluctuati ons and has provided evidence of a second, apparently distinct, source of disorder. While the origin of this disorder is not fully understoo d, the data are consistent with simple lifetime broadening of the quas iparticle states.