Electromagnetic characteristics of bilayer quantum Hall systems in the presence of interlayer coherence and tunneling

TL;DR

This paper develops a long-wavelength effective theory for bilayer quantum Hall systems with interlayer coherence, clarifying their electromagnetic response and the nature of low-lying collective modes, while critically examining standard Chern-Simons approaches.

Contribution

It introduces a pseudospin-texture effective theory and algebraic single-mode approximation to analyze electromagnetic characteristics and collective modes in bilayer quantum Hall systems.

Findings

Gauge invariance is maintained in the response functions.

The Meissner effect is absent in these systems.

The theory clarifies the nature of low-lying neutral collective modes.

Abstract

The electromagnetic characteristics of bilayer quantum Hall systems in the presence of interlayer coherence and tunneling are studied by means of a pseudospin-texture effective theory and an algebraic framework of the single-mode approximation, with emphasis on clarifying the nature of the low-lying neutral collective mode responsible for interlayer tunneling phenomena. A long-wavelength effective theory, consisting of the collective mode as well as the cyclotron modes, is constructed. It is seen explicitly from the electromagnetic response that gauge invariance is kept exact, this implying, in particular, the absence of the Meissner effect in bilayer systems. Special emphasis is placed on exploring the advantage of looking into quantum Hall systems through their response; in particular, subtleties inherent to the standard Chern-Simons theories are critically examined.