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Bertrand Halperin explained the role of conducting edge states in the quantum Hall effect. A two-dimensional sample can have localized states in its interior while current-carrying states extend along its boundary. The resulting picture connects an integer Hall response with the way electronic states traverse the sample, rather than relying only on a bulk transport formula. It clarifies why disorder and localization do not automatically destroy a quantized plateau.[ref]
Quantized Hall conductance, current-carrying edge states, and the existence of extended states in a two-dimensional disordered potential by B. I. Halperin. Physical Review B 25, 2185 (1982), edge states and disordered two-dimensional system
Portrait of Bertrand Halperin
. Betsy Devine. CC BY-SA 3.0, via Wikimedia Commons. Source.