Theory of Current-Induced Breakdown of the Quantum Hall Effect
  By studying the quantum Hall effect of stationary states with high values of injected current using a von Neumann lattice representation, we found that broadening of extended state bands due to a Hall electric field occurs and causes the breakdown of the quantum Hall effect. The Hall conductance agrees with a topological invariant that is quantized exactly below a critical field and is not quantized above a critical field. The critical field is proportional to $B^{3/2}$ and is enhanced substantially if the extended states occupy a small fraction of the system. 
Kenzo Ishikawa, Nobuki Maeda, Tetsuyuki Ochiai, and Hisao Suzuki