QED$_{2+1}$ with Nonzero Fermion Density and Quantum Hall Effect
  A general expression for the conductivity in the QED$_{2+1}$ with nonzero fermion density in the uniform magnetic field is derived. It is shown that the conductivity is entirely determined by the Chern-Simons coefficient: $\sigma_{ij}=\varepsilon_{ij}~{\cal C}$ and is a step-function of the chemical potential and the magnetic field. 
Vadim Zeitlin