# Geometric Origin of Phonon Magnetic Moment in Dirac Materials

**Authors:** Wenqin Chen, Xiao-Wei Zhang, Ting Cao, Shi-Zeng Lin, Di Xiao  
**arXiv:** [2505.09732](https://arxiv.org/abs/2505.09732)  
**Date:** 2025-05-14  
**Summary page:** https://www.summarizepaper.com/en/paper/2505.09732v1/

## Key points

- Chen et al. develop a comprehensive theory for understanding the phonon magnetic moment in doped Dirac materials
- Phonons are approached as emergent gauge and gravitational fields coupled to Dirac fermions within curved space
- Phonon moment arises from two distinct mechanisms: one proportional to electron Hall conductivity through emergent gauge field coupling, and another linked to Hall viscosity through frame field coupling
- Theoretical framework applied to Cd$_3$As$_2$ shows quantitative agreement with experimental observations, validating the theory and unveiling a general mechanism for generating substantial phonon magnetism in metallic systems
- Findings suggest a novel avenue for investigating Hall viscosity through phonon dynamics, contributing to our understanding of the interplay between phonons, electrons, and geometric properties in materials with Dirac-like characteristics

## Summary

In their study titled "Geometric Origin of Phonon Magnetic Moment in Dirac Materials," Chen et al. develop a comprehensive theory for understanding the phonon magnetic moment in doped Dirac materials. They approach phonons as emergent gauge and gravitational fields that are coupled to Dirac fermions within curved space. By categorizing electron-phonon coupling into angular momentum channels of Fermi surface deformation, the researchers demonstrate that the phonon moment arises from two distinct mechanisms: one proportional to the electron Hall conductivity through emergent gauge field coupling, and another linked to the Hall viscosity through frame field coupling. Applying their theoretical framework to Cd$_3$As$_2$ using first-principles calculations, Chen et al. achieve quantitative agreement with experimental observations. This successful application not only validates their theory but also unveils a general mechanism for generating substantial phonon magnetism in metallic systems. Furthermore, their findings suggest a novel avenue for investigating Hall viscosity through phonon dynamics. is an important phenomenon in , which has been extensively studied by researchers such as Chen et al. In their study, they propose a novel approach by considering  and . By categorizing this coupling into different angular momentum channels of Fermi surface deformation, they are able to explain the origin of phonon magnetic moments in doped Dirac materials. Their theoretical framework is further supported by first-principles calculations on Cd$_3$As$_2$, which show quantitative agreement with experimental results. This not only validates their theory but also provides insights into how substantial phonon magnetism can be generated in metallic systems. Moreover, their findings also suggest a new avenue for studying  through phonon dynamics. This is significant as it adds to our understanding of the intricate interplay between phonons, electrons, and geometric properties in materials with Dirac-like characteristics. The study also references prior research on related topics such as torsional anomalies, hall viscosity, topological response in Weyl semimetals, and hydrodynamic electron flow. These references provide additional context and support for the theoretical framework proposed by Chen et al., enhancing our understanding of phonon magnetic moments in Dirac materials. In conclusion, this research contributes significantly to the field of condensed matter physics by shedding light on the complex nature of phonon magnetic moments in . It not only provides a comprehensive theory but also suggests new avenues for further exploration and investigation.