Abstract
We study edge transport in a simple model of a constricted quantum Hall system with a lowered local filling factor. The current backscattered from the constriction is explained from a matching of the properties of the edge-current excitations in the constriction (ν2) and bulk (ν1) regions. We develop a hydrodynamic theory for bosonic edge modes inspired by this model, finding that a competition between two tunneling process, related by a quasiparticle-quasihole symmetry, determines the fate of the low-bias transmission conductance. A novel generalisation of the Kane-Fisher quantum impurity model is found, describing transitions from a weak-coupling theory at partial transmission to strong-coupling theories for perfect transmission and reflection as well as a new symmetry dictated fixed point. These results provide satisfactory explanations for recent experimental results at filling factors of 1/3 and 1.
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