Line junctions in the quantum Hall effect

Abstract

A long narrow gate across a fractional quantum Hall fluid at filling $\ensuremath{\nu}=1/m$ with odd integer $m$, creates a one-dimensional (1D) system that is isomorphic to a disordered 1D electron gas with attractive interactions. By varying the gate potential along such a line junction, it should be possible to tune through the 1D localization transition, predicted for an attractively interacting electron gas. The key signature of this 1D metal-insulator transition is the temperature dependence of the conductivity, which diverges as a power of temperature in the metallic phase, and vanishes rapidly in the insulator. We show that the 1D conductivity can be extracted from a standard Hall transport measurement, in the regime where the Hall conductance is close to its quantized value. A line junction in a $\ensuremath{\nu}=2/3$ quantized Hall fluid is predicted to exhibit a similar localization transition.