Geometric Origin of Phonon Magnetic Moment in Dirac Materials

TL;DR

This paper presents a theoretical framework linking phonon magnetic moments in doped Dirac materials to emergent gauge and gravitational fields, with applications to Cd$_3$As$_2$ and implications for probing Hall viscosity.

Contribution

It introduces a novel theory connecting phonon magnetism to Hall conductivity and viscosity in Dirac materials, supported by first-principles calculations and experimental agreement.

Findings

Phonon magnetic moment arises from gauge and gravitational couplings.

Quantitative agreement with experiments on Cd$_3$As$_2$.

Proposes a new method to probe Hall viscosity via phonon dynamics.

Abstract

We develop a theory for the phonon magnetic moment in doped Dirac materials, treating phonons as emergent gauge and gravitational fields coupled to Dirac fermions in curved space. By classifying electron-phonon coupling into angular momentum channels of Fermi surface deformation, we show that the phonon moment arises from two mechanisms: proportional to the electron Hall conductivity through the emergent gauge field coupling, and to the Hall viscosity through the frame field coupling. Applying our theory to Cd$_3$As$_2$ with first-principles calculations, we find quantitative agreement with experiment. Our results reveal a general mechanism for dynamically generating large phonon magnetism in metals and suggest a new route for probing Hall viscosity via phonon dynamics.