Quantum Coherence and W_infty*SU(2) Algebra in Bilayer Quantum Hall Systems

TL;DR

This paper explores the quantum coherence phenomena in bilayer quantum Hall systems by mapping them to monolayer systems, revealing a W_infty*SU(2) symmetry and constructing a Landau-Ginzburg theory with topological Skyrmion excitations.

Contribution

It introduces a novel symmetry analysis and a Landau-Ginzburg framework for bilayer quantum Hall systems, highlighting the role of W_infty*SU(2) symmetry and Skyrmion excitations.

Findings

Identification of W_infty*SU(2) symmetry in bilayer QH systems

Construction of a Landau-Ginzburg theory for the coherent mode

Detection of Skyrmion excitations via Hall current measurements

Abstract

We analyze the bilayer quantum Hall (QH) system by mapping it to the monolayer QH system with spin degrees of freedom. By this mapping the tunneling interaction term is identified with the Zeeman term. We clarify the mechanism of a spontaneous development of quantum coherence based on the Chern-Simons gauge theory with the lowest-Landau-Level projection taken into account. The symmetry group is found to be W_infty*SU(2), which says that the spin rotation affects the total electron density nearby. Using it extensively we construct the Landau-Ginzburg theory of the coherent mode. Skyrmion excitations are topological solitons in this coherent mode. We point out that they are detectable by measuring the Hall current distribution.