Gauge theory of giant phonon magnetic moment in doped Dirac semimetals

We present a quantum theory for phonon magnetic moment in doped Dirac semimetals. Our theory is based on an emergent gauge field approach to the electron-phonon coupling, applicable for 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 Cd₃ As₂. Our results provide practical guidance for the dynamic generation of large magnetization in the topological quantum materials.