On the gauge invariant and topological nature of the localization   determining the Quantum Hall Effect plateaus
  It is shown how the electromagnetic response of the 2DEG under Quantumm Hall Effect regime, chracterized by the Chern-Simons topological action, transforms the sample impurities and defects in charge reservoirs that stabilize the the Hall conductivity plateaus. The results, determine the basic dynamical origin of the singular properties of localization under the occurrence of the QHE obtained in the pioneering works of Laughlin and of Joynt and Prange, by means of a gauge invariance argument and a purely electronic analysis, respectively. The common picture of electrons moving the equipotential lines gets an analytical realization through the Chern-Simons current and charge densities. 
Alejandro Cabo Montes de Oca and Danny Martinez-Pedrera