Electron Localization in the Quantum Hall Regime

The theory of the insulating state discriminates between insulators and metals by means of a localization tensor, which is finite in insulators and divergent in metals. In absence of time-reversal symmetry, this same tensor acquires an off-diagonal imaginary part, proportional to the dc transverse conductivity, leading to quantization of the latter in two-dimensional systems. I provide evidence that electron localization—in the above sense—is the common cause for both vanishing of the dc longitudinal conductivity and quantization of the transverse one in quantum Hall fluids.