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.