Effect of screening of the Coulomb interaction on the conductivity in the quantum Hall regime.

We study variable-range hopping in the quantum Hall effect regime in the presence of a metallic gate parallel to the plane of a two-dimensional electron gas. Screening of the Coulomb interaction by the gate causes the partial ``filling'' of the Coulomb gap in the density of localized states. At low enough temperatures this leads to a substantial enhancement and a different temperature behavior of the hopping conductivity. As a result, the diagonal conductivity peaks become much wider. The power-law dependence of the width of the peaks on the temperature changes: the corresponding exponent turns out to be twice as small as that for gateless structures. The width dependences on the current in the non-Ohmic regime and on the frequency for the absorption of the electromagnetic waves experience a similar modification. The experimental observation of the crossovers predicted may demonstrate the important role of the Coulomb interaction in the integer quantum Hall regime.