Nonlinear screening and percolative transition in a two-dimensional electron liquid

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A novel variational method is proposed for calculating the percolation threshold, the real-space structure, and the thermodynamical compressibility of a disordered two-dimensional electron liquid. Its high accuracy is verified against prior numerical results and newly derived exact asymptotics. The inverse compressibility is shown to have a strongly asymmetric minimum at a density that is approximately the triple of the percolation threshold. This implies that the experimentally observed metal-insulator transition takes place well before the percolation point is reached.