Anomalous Hall Effect in non-commutative mechanics

P. A. Horvathy

Anomalous Hall Effect in non-commutative mechanics

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arxiv cond-mat/0606472 v3 pith:RB76NBHF submitted 2006-06-18 cond-mat.mes-hall hep-th

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The anomalous velocity term in the semiclassical model of a Bloch electron deviates the trajectory from the conventional one. When the Berry curvature (alias noncommutative parameter) is a monopole in momentum space as found recently in some ferromagnetic semiconductors while observing the anomalous Hall effect, we get a transverse shift, similar to that in the optical Hall effect.

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Peierls substitution and Hall motion in exotic Carroll dynamics
hep-th 2024-11 accept novelty 5.0 of 10

Exotic Carroll particles with two-parameter central extension move by an anomalous Hall law, and their critical reduction reproduces the Dunne-Jackiw-Trugenberger model underlying the Peierls substitution.

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