Origin of Giant Phonon Magnetic Moment in Orbital Seebeck Effect: a Heisenberg-type L-L Coupling

Abstract: Inspired by the recent observation of the orbital Seebeck effect in alpha-quartz, we identify an intrinsic amplification mechanism for thermally generated phonon angular momentum and phonon magnetic moment in chiral insulators. We propose a Heisenberg-type long-range coupling between phonon angular momenta, referred to here as L-L coupling, which opens a self-consistent feedback channel and strongly enhances the bare thermal response within linear response. Our calculations reveal a pronounced temperature- and size-dependent amplification, dominated by the off-diagonal channel, with the total phonon angular momentum enhanced by up to nearly two orders of magnitude as the system approaches the threshold from below. These findings suggest that L-L coupling may provide a microscopic origin of giant phonon magnetic moment the recently observed orbital Seebeck effect in alpha-quartz.