A quantum Hall edge state is confined across a boundary but can extend along it and carry electric current. B. I. Halperin related these current-carrying boundary states to quantized Hall transport in a disordered two-dimensional system.[ref]
Quantized Hall conductance, current-carrying edge states, and the existence of extended states in a two-dimensional disordered potential by B. I. Halperin. Publisher abstract: transverse confinement, perimeter extension and current
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