Fig. 4.

Many-body gaps through capacitance measurements. (A) C(V) for one of our devices at B = 12 T and 3 K (blue curve). Red curve: the corresponding changes in μ. Yellow shaded areas mark the regions of negative compressibility. (B) Energy gaps found for different ν. Symbols correspond to alternative methods of determining Δ. Solid symbols: by using temperature dependence of the capacitance minima; crossed symbols: from steps in μ as shown in A; open symbols: from magnetic field dependence of the minima’s positions. Blue circles: ν = 2 (similar results for ν = −2); magenta squares: ν = 0; olive triangles: ν = ±1. Green curve: expected cyclotron gap for v_F = 1.05 × 10⁶ m/s; red curve: same but using the renormalized values of v_F(n); orange: Coulomb energy e²/4πɛl_b, where l_b = (h/2πeB)^1/2 is the magnetic length. (C) Recovery of quantum capacitance from negative to positive with increasing high B. For this device, d = 28 nm; 2 K. Black curve corresponds to d/l_b ∼3.8; red: 4.5; green: 5.1; blue: 5.9.