The Study of Goldstone Modes in $\nu$=2 Bilayer Quantum Hall Systems

TL;DR

This paper systematically derives the effective Hamiltonian for Goldstone modes in bilayer quantum Hall systems at filling factor 2, analyzing their dispersion relations across different phases and exploring phase coherence in the zero tunneling limit.

Contribution

It introduces a systematic method to derive the effective Hamiltonian for Goldstone modes in various phases of the $ u$=2 bilayer quantum Hall system.

Findings

Identifies a gapless mode with linear dispersion in the CAF phase.

Analyzes dispersion relations and coherence lengths of Goldstone modes.

Explores phase coherence in the zero tunneling limit.

Abstract

At the filling factor $\nu$=2, the bilayer quantum Hall system has three phases, the spin-ferromagnet phase, the spin singlet phase and the canted antiferromagnet (CAF) phase, depending on the relative strength between the Zeeman energy and interlayer tunneling energy. We present a systematic method to derive the effective Hamiltonian for the Goldstone modes in these three phases. We then investigate the dispersion relations and the coherence lengths of the Goldstone modes. To explore a possible emergence of the interlayer phase coherence, we analyze the dispersion relations in the zero tunneling energy limit. We find one gapless mode with the linear dispersion relation in the CAF phase.