``Splitting'' of Delocalized States in a Double--Layer System in a Strong Magnetic Field

Abstract

A double--layer system in a strong perpendicular magnetic field is considered. We assume a random potential in each layer to be smooth. We also assume that there is no correlation between random potentials in different layers. Under these conditions the equipotential lines from different layers, corresponding to the same energy, may cross each other. We show that, if the tunnel coupling between the layers exceeds some characteristic value (which is much smaller than the width of the Landau level), then the probability for an electron to switch equipotential (and, thus, the layer) at the intersection is close to one. As a result, the structure of each delocalized state in a double--layer system becomes completely different from that for an isolated layer. The state is composed of alternating pieces of equipotentials from different planes. These combined equipotentials form a percolation network. We demonstrate that the regions, where equipotentials from different planes touch each other, play the role of saddle points for such a network. The energy separation between two delocalized states is of the order of the width of the Landau level, and the critical exponent of the localization length is $7/3$--the same as for an isolated layer.