Gauge theory of giant phonon magnetic moment in doped Dirac semimetals

We present a quantum theory of phonon magnetic moment in doped Dirac semimetals. Our theory is based on an emergent gauge field approach to the electron-phonon coupling, applicable to both gapless and gapped systems. We find that the magnetic moment is directly proportional to the electrical Hall conductivity through the phonon Hall viscosity. Our theory is combined with the first-principles calculations, allowing us to quantitatively implement it to realistic materials. Magnetic moments are found to be on the order of Bohr magneton for certain phonon modes in graphene and ${\text{Cd}}_3{\text{As}}_2$. Our results provide practical guidance for the dynamical generation of large magnetization in the topological quantum materials.