Coadjoint-orbit bosonization shows the de Haas-van Alphen phase shift is governed by the static anomalous Hall conductance, with Berry-curvature corrections to the Lifshitz-Kosevich amplitude.
Shoenberg, Magnetic Oscillations in Metals , Cam- bridge Monographs on Physics (Cambridge University Press, 1984)
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Berry Phase and Quantum Oscillation from Multi-orbital Coadjoint-orbit Bosonization
Coadjoint-orbit bosonization shows the de Haas-van Alphen phase shift is governed by the static anomalous Hall conductance, with Berry-curvature corrections to the Lifshitz-Kosevich amplitude.