Comparison between the compressibilities of the zero field and composite-fermion metallic states of the two-dimensional electron system

We have studied the capacitance between a two-dimensional electron system and a gate of field-effect transistors, produced from three different wafers with a single remotely doped $\mathrm{GaAs}/{\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ heterojunction. In the vicinity of the Landau-level filling factor $\nu =1/2,$ the increment of the capacitance relative to its zero-magnetic-field value, $\delta C_{1/2},$ was found to be insensitive to the carrier density, and close to the value as if the particles are noninteracting. This observation implies that electron-electron interaction affects the compressibility of the zero-field and composite-fermion metallic states in a very similar manner.