Composite bosons in bilayer nu = 1 system: An application of the Murthy-Shankar formalism

TL;DR

This paper applies the Murthy-Shankar Chern-Simons formalism to calculate the out-of-phase mode dispersion in bilayer quantum Hall systems at nu=1, showing good agreement with pseudospin models and exploring effects of layer imbalance.

Contribution

It adapts the Murthy-Shankar formalism to bilayer nu=1 systems, accurately capturing mode dispersion and layer imbalance effects.

Findings

Mode at zero layer separation matches pseudospin predictions.

Mode velocity depends linearly on layer separation d.

Formalism allows analysis of fluctuations and imbalanced layers.

Abstract

We calculate the dispersion of the out-of-phase mode characteristic for the bilayer nu = 1 quantum Hall system applying the version of Chern-Simons theory of Murthy and Shankar that cures the unwanted bare electron mass dependence in the low-energy description of quantum Hall systems. The obtained value for the mode when d, distance between the layers, is zero is in a good agreement with the existing pseudospin picture of the system. For d nonzero but small we find that the mode is linearly dispersing and its velocity to a good approximation depends linearly on d. This is in agreement with the Hartree-Fock calculations of the pseudospin picture that predicts a linear dependance on d, and contrary to the naive Hartree predictions with dependence on the square-root of d. We set up a formalism that enables one to consider fluctuations around the found stationary point values. In addition we address the case of imbalanced layers in the Murthy-Shankar formalism.