Magnetic moment of phonons in graphene induced by a magnetic field

A magnetic field not only changes the electronic structure in graphene but also affects the phonon excitations via the electron-phonon interaction and even enables the phonons to generate magnetism. In this paper, we evaluate the magnetic moment of phonons in graphene using a generating-functional technique. The calculation results indicate that the phonon magnetic moment exists only in a weak magnetic field. The step-like change of the magnetic moment with the magnetic field reflects a macroscopic quantum effect.