Theoretical analysis demonstrates quantized Hall conductivity in two-dimensional systems through gauge invariance and mobility gaps, indicating exact quantization immune to edge effects.
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.
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R. B. Laughlin (1981) studied this question.
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