Phonon with a large magnetic moment in topological materials

The Born-Oppenheimer approximation assumes an adiabatic evolution of electronic states following ions’ motion. During the evolution, the electronic state can collect nontrivial geometrical phases. In response to a circularly polarized phonon, the geometrical phase leads to a topological magnetic moment expressed in a second Chern form [arXiv: 2103.05786]. This refines the Born effective charge to be k-resolved and reveals the essential role of the phonon modified boundary current that is related to the momentum space Berry curvature. When a Yang's monopole presents near the parameter space of interest, the second Chern form can diverge, resulting in a large phonon magnetic moment. Topological insulators/semimetals generally host phonons with a large magnetic moment. Our results agree with recent experiments.