It is shown that the quantization of the Hall conductivity of two-dimensional metals which has been observed recently by Klitzing, Dorda, and Pepper and by Tsui and Gossard is a consequence of gauge invariance and the existence of a mobility gap. Edge effects are shown to have no influence on the accuracy of quantization. An estimate of the error based on thermal activation of carriers to the mobility edge is suggested.

• Received 20 January 1981

DOI:https://doi.org/10.1103/PhysRevB.23.5632

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Physical Review B 50^th Anniversary Milestones

These Milestone studies represent lasting contributions to physics by way of reporting significant discoveries, initiating new areas of research, or substantially enhancing the conceptual tools for making progress in the burgeoning field of condensed matter physics.