Quantal Heating of 2D electrons in strong magnetic fields

Usually heating of conducting electrons by $dc$ electric field increases electron temperature and effects weakly the electron transport. In this report we show that the $dc$ heating of 2D electrons with a quantized spectrum is very peculiar and violates strongly the Ohm's Law [1]. The quantal heating establishes nontrivial electron distribution, which has the same broadening or an effective ``temperature'' as the unbiased system. The heating reduces significantly the dissipative electron transport, forcing the quantum conductors into a state with zero differential resistance (ZDR). Furthermore an apparent $dc$ driven metal-insulator transition is found, which correlates with the transition into the ZDR state. This interesting correlation is unexpected and is not understood.\\[4pt] [1] J.-Q. Zhang, S.A. Vitkalov and A.A. Bykov, Phys. Rev. B 80, 045310 (2009); S. A. Vitkalov, International Journal of Modern Physics B, 23, 4727 (2009).