We perform combined resistivity and compressibility studies of two-dimensional hole and electron systems which show the apparent metal-insulator transition -a crossover in the sign of ∂R/∂T with changing density. No thermodynamic anomalies have been detected in the crossover region. Instead, despite a ten-fold difference in rs, the compressibility of both electrons and holes is well described by the theory of nonlinear screening of the random potential. We show that the resistivity exhibits a scaling behavior near the percolation threshold found from analysis of the compressibility. Notably, the percolation transition occurs at a much lower density than the crossover. The apparent metal-insulator transition (MIT) in high-mobility two-dimensional systems remains a topic of fundamental interest [1] and continuing debate [2]. The anomaly of these systems is exemplified by the existence of a narrow range of carrier densities around n = n c where the slope of the temperature dependence of the resistance, ∂R/∂T , changes its sign. To unravel a complex interplay between interactions and disorder in this phenomenon, it is essential to combine transport measurements with other experimental probes, in particular measurements of the thermodynamic density of states (also referred to as the charge compressibility [3, 4]) χ = dn/dµ, where µ is the chemical potential. There have been only few measurements of χ near the apparent MIT [5,6,7], among which work [5] on a 2D hole gas with large values of the Coulomb interaction parameter r s ≡ 1/ πna 2 B ≈ 5 − 16 has attracted much attention. (Here a B = 18Å is the effective Bohr radius for the hole mass of 0.38 m 0 .) In their experiments done at T = 0.3 − 1.3 K the authors of Ref. [5] found that the inverse compressibility χ −1 (n) has a minimum which is positioned exactly at n c . This was interpreted as a thermodynamic signature of an interaction-driven phase transition discussed in theoretical works [8,9].An alternative explanation of the minimum of χ −1 (n) can be based on the nonlinear screening theory (NST) [10,11,12,13] that emphasizes the role of disorder. The basic premise of the NST is that a low-density metal is unable to screen fluctuations of potential, so that depletion regions with vanishingly small local density appear and grow as n decreases. The NST predicts that χ −1 (n) has a minimum at n = n m (determined by disorder), and a rapid upturn to positive values at n < n m .This theory also predicts a percolation threshold at n = n p [11], where n p ≈ n m /3 in typical GaAs systems [13]. There have been suggestions, based on the conductance scaling, that the percolation transition is closely related to the change in the sign of ∂R/∂T [12,14,15]. (The existence of the percolative MIT in 2D GaAs structures was proposed earlier in [11].) In this work we use combined compressibility and conductance measurements to shed light on the origin of the apparent MIT in 2D hole gases with large interactions between the carriers -a problem widely debated over the last few years...
