What question did this study set out to answer?

To provide a theoretical explanation for the exact quantization of Hall conductivity observed in two-dimensional metals.

May 15, 1981Physical review. B, Condensed matter

Quantized Hall conductivity in two dimensions

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Authors

RLR. B. LaughlinStanford University

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Implication

Theoretical analysis demonstrates quantized Hall conductivity in two-dimensional systems through gauge invariance and mobility gaps, indicating exact quantization immune to edge effects.

Key Points

To provide a theoretical explanation for the exact quantization of Hall conductivity observed in two-dimensional metals.
Applied gauge invariance principles to two-dimensional electron systems subject to strong magnetic fields.
Evaluated the impact of localized electronic states across a mobility gap and the influence of sample boundaries.
Formulated error estimates for Hall conductivity quantization based on thermal activation across the mobility edge.
Hall conductivity quantization is shown to arise directly from gauge invariance combined with the existence of a mobility gap.
Sample edge effects are demonstrated to have no detrimental influence on the accuracy of conductivity quantization.
Deviations from perfect quantization are limited to the thermal activation of charge carriers to the mobility edge.

Cite This Study

R. B. Laughlin (1981) studied this question.

synapsesocial.com/papers/69dc495745b398e6439f570e https://doi.org/10.1103/physrevb.23.5632

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Implication

Theoretical analysis demonstrates quantized Hall conductivity in two-dimensional systems through gauge invariance and mobility gaps, indicating exact quantization immune to edge effects.

Quantized Hall conductivity in two dimensions

Discussion

Member takes

Implication

Key Points

Cite This Study

Quantized Hall conductivity in two dimensions

Discussion

Member takes

Implication

Key Points

Cite This Study

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