Single-mode approximation and effective Chern-Simons theories for quantum Hall systems

TL;DR

This paper develops a unified framework linking the single-mode approximation with Chern-Simons theories to describe elementary and collective excitations in quantum Hall systems, highlighting differences between single-layer and bilayer systems.

Contribution

It demonstrates that the SMA generally produces a variant of the bosonic Chern-Simons theory as an effective description for quantum Hall excitations, with specific deviations in bilayer systems.

Findings

SMA yields a Chern-Simons type effective theory for quantum Hall systems.

Long-wavelength agreement with standard Chern-Simons theory in single-layer systems.

Detectable out-of-phase excitations in bilayer systems via Hall-drag experiments.

Abstract

A unified description of elementary and collective excitations in quantum Hall systems is presented within the single-mode approximation (SMA) framework, with emphasis on revealing an intimate link with Chern-Simons theories. It is shown that for a wide class of quantum Hall systems the SMA in general yields, as an effective theory, a variant of the bosonic Chern-Simons theory. For single-layer systems the effective theory agrees with the standard Chern-Simons theory at long wavelengths whereas substantial deviations arise for collective excitations in bilayer systems. It is suggested, in particular, that Hall-drag experiments would be a good place to detect out-of-phase collective excitations inherent to bilayer systems. It is also shown that the intra-Landau-level modes bear a similarity in structure (though not in scale) to the inter-Landau-level modes, and its implications on the composite-fermion and composite-boson theories are discussed.