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
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.
PACS: 73.43.-f – Quantum Hall effects / 74.20.Fg – BCS theory and its development / 11.15.-q – Gauge field theories
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2006