Critical Resistivity along the Quantum Hall Liquid--Insulator Transition Line

The critical resistivity measured along the quantum Hall liquid–insulator transition line indicates a pronounced peak at a critical filling factor close to 1, which marks the crossover from the high to low magnetic field regime in the phase diagram. The origin of this behavior is explained in the framework of classical transport in a puddle network model. The proposed scenario is also consistent with the behavior of the critical Hall resistance along the transition line. In addition, a formula is suggested as a fit for isotherms (${\rho }_{xx}$ vs. $\nu$) in the moderately high field regime, which exhibits a violation of duality symmetry as the critical resistivity is evelated from the `universal’ value $h\mathrm{/}{e}^2$.