Phonon Magnetic Moment from Electronic Topological Magnetization

Abstract

The traditional theory of magnetic moments for chiral phonons is based on the picture of the circular motion of the Born effective charge, typically yielding a small fractional value of the nuclear magneton. Here we investigate the adiabatic evolution of electronic states induced by lattice vibration of a chiral phonon and obtain an electronic orbital magnetization in the form of a topological second Chern form. We find that the traditional theory needs to be refined by introducing a $\mathbf{k}$ resolved Born effective charge, and identify another contribution from the phonon-modified electronic energy together with the momentum-space Berry curvature. The second Chern form can diverge when there is a Yang's monopole near the parameter space of interest as illustrated by considering a phonon at the Brillouin zone corner in a gaped graphene model. We also find large magnetic moments for the optical phonon in bulk topological materials where non-topological contribution is also important. The magnetic moment experiences a sign change when the band inversion happens.

arXiv comment5 pages, 3 figs, comments are welcome

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• Lattice dynamics with molecular Berry curvature: chiral optical phonons
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• Dynamic electron-phonon and spin-phonon interactions due to inertia
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• Weyl Phonons: The connection of topology and chirality
• Chiral phonons as dark matter detectors
• Abnormal Phonon Angular Momentum due to Off-diagonal Elements in Density Matrix induced by Temperature Gradient
• Topological phonons in an inhomogeneously strained silicon-5: Inhomogeneous magnetoelectronic effect in a conductor