Thermodynamic Signature of a Two-Dimensional Metal-Insulator Transition

We present a study of the compressibility, K, of a two-dimensional hole system which exhibits a metal-insulator phase transition at zero magnetic field. It has been observed that dK/dp changes sign at the critical density for the metal-insulator transition. Measurements also indicate that the insulating phase is incompressible for all values of B. Finally, we show how the phase transition evolves as the magnetic field is varied and construct a phase diagram in the density-magnetic field plane for this system.