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

TL;DR

This paper investigates how strong interlayer coupling in a double-layer quantum Hall system alters the structure of delocalized states, leading to a percolation network formed by combined equipotential lines from both layers.

Contribution

It demonstrates that above a certain tunneling threshold, delocalized states become interconnected across layers, fundamentally changing their structure compared to isolated layers.

Findings

Delocalized states form a percolation network of alternating equipotentials.

Interlayer tunneling causes equipotential lines to cross and mix between layers.

Critical exponent of localization length remains at 7/3, same as in single-layer systems.

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.