Eur. Phys. J. B 54, 157-168 (2006)
https://doi.org/10.1140/epjb/e2006-00436-x

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

¹ Institute for Solid State Physics, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba, 277-8581, Japan
² Department of Physics, Hokkaido University, Sapporo, 060-0810, Japan

Corresponding author: ^a tao@issp.u-tokyo.ac.jp

Received: 15 May 2006
Revised: 30 August 2006
Published online: 8 December 2006

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.