Induced Chern-Simons term of a paired electron state in the quantum Hall system

TL;DR

This paper calculates the induced Chern-Simons term in a paired electron state within a quantum Hall system, revealing correction terms linked to symmetry breaking and topological properties of the gap function.

Contribution

It introduces a field theory approach on the von Neumann lattice to compute the Chern-Simons term, including novel correction terms from symmetry breaking effects.

Findings

The Hall conductance includes correction terms from symmetry breaking.

Correction terms are connected to a topological number of the gap function.

The Nambu-Goldstone mode influences the Chern-Simons coefficient.

Abstract

The induced Chern-Simons term for a paired electron state is calculated in the quantum Hall system by using a field theory on the von Neumann lattice. The coefficient of the Chern-Simons term, which is the Hall conductance, has not only the usual term proportional to a filling factor due to P (parity) & T (time reversal) symmetry breaking but also correction terms due to P & T & U(1) symmetry breaking. The correction term essentially comes from the Nambu-Goldstone mode and depends on an infrared limit. It is shown that the correction term is related to a topological number of a gap function in the momentum space.