O ct 1 99 5 Evidence for charge - flux duality near the quantum Hall liquid to insulator transition

We examine the longitudinal, non-linear, current-voltage characteristics near the quantum Hall liquid to insulator transition and show that a simple mapping exists between the characteristics on the quantum Hall side and those on the insulating side of the transition. More precisely, at filling factors related by the law of corresponding states the current and voltage simply trade places. We interpret these observations as evidence for the existence, in the composite boson description, of charge-flux duality near disorder dominated transitions in quantum Hall systems. 1 The quantum Hall effect (QHE) has long been understood to involve the intertwining of the elegant physics of the ideal states with the equally elegant physics of localization. The precise nature of the intertwining has been somewhat controversial, for it involves solving a problem with interactions, fractional statistics and disorder—a somewhat formidable mix. Nevertheless, considerable theoretical and experimental progress had been made in recent years in understanding the phase diagram of QH states and the transitions between them. On the theoretical front, Kivelson, Lee and Zhang (KLZ) [1] used a flux attachment (Chern-Simons) transformation [2], to map the two dimensional electron system (2DES) at a magnetic field (B) onto a bosonic system under a different field B ef f. The advantage of this mapping is clear if one considers the " magic " Landau level filling factors (ν's) where the fractional quantum Hall effect (FQHE) liquid states are observed. At these ν's the Chern Simons gauge field cancels, on average, the externally applied B, and the composite bosons (CB) experience a vanishing B ef f. The incompressible FQHE states then arise as a result of the formation of a Bose-condensed, superconducting, state of the CB's. At ν's other than the magic ν's, the cancellation of the external B is not exact and, according to this bosonic picture, vortices are created in the CB condensate. For small deviations from magic ν's the vortex density is small, they are localized by disorder and do not contribute to the long wavelength electrical response. When the deviation from the magic ν's becomes sufficiently large the superconductivity of the bosons is destroyed by the excess magnetic field and they turn insulating. This results in a transition to an insulating, or a different quantum Hall, state. Utilizing this bosonic formulation, KLZ derived a " law of corresponding states " which relates the different QH states and allows construction of a phase diagram …