Percolation and the electron–electron interaction in an array of antidots

A square lattice of microcontacts with a period of 1 μm in a dense low-mobility two-dimensional electron gas is studied experimentally and numerically. At the variation of the gate voltage V g , the conductivity of the array varies by five orders of magnitude in the temperature range T from 1.4 to 77 K in good agreement with the formula σ(V g ) = (V g −V g * (T))β with β = 4. The saturation of σ(T) at low temperatures is absent because of the electron–electron interaction. A random-lattice model with a phenomenological potential in microcontacts reproduces the dependence σ(T, V g ) and makes it possible to determine the fraction of microcontacts x(V g , T) with conductances higher than σ. It is found that the dependence x(V g ) is nonlinear and the critical exponent in the formula σ ∝ − (x - 1/2) t in the range 1.3 < t(T, V g ) < β.