Thermodynamic Compressibility of a Two-Dimensional Electron System: Signature of a Droplet State

We have used a field-penetration method to measure thermodynamic compressibility of a moderately interacting two-dimensional electron system ($r_{s}$ $approx$ 0.5-3) in a three terminal GaAs/AlGaAs device, fabricated with an epitaxial lift-off technique. We found that the density and temperature dependencies of the compressibility are qualitatively different from that observed in earlier studies of the 2D hole system, where interaction energies are considerably stronger. We show that the observed characteristics can be described by the recently developed formalism for compressibility of the droplet state.