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

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.

arXiv comment26 pages, 6 figures

References in corpus (15)

• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Evidence for an Anisotropic State of Two-Dimensional Electrons in High Landau Levels
• Charge Density Wave in Two-Dimensional Electron Liquid in Weak Magnetic Field
• Superfluid analogies of cosmological phenomena
• Strongly Anisotropic Electronic Transport at Landau Level Filling Factor $\nu =9/2$ and $\nu =5/2$ Under Tilted Magnetic Field
• Observation of Induced Chern-Simons Term in P- and T- violating Superconductors
• Gauge Invariance, Finite Temperature and Parity Anomaly in D=3
• Effective Action and Renormalization Group Flow of Anisotropic Superconductors
• Vortex with Fractional Quantum Numbers in Chiral p-Wave Superconductor
• Compressible Anisotropic States around the Half-Filled Landau Levels
• On the Coleman-Hill Theorem
• Field Theory on the von Neumann Lattice and the Quantized Hall Conductance of Bloch Electrons
• Integer Quantum Hall Effect with Realistic Boundary Condition : Exact Quantization and Breakdown
• Effective Hamiltonian for striped and paired states at the half-filled Landau level
• Intra-Landau level polarization effect for a striped Hall gas