Theory of giant phonon magnetic moment in doped Dirac semimetals

We propose a new theoretical framework to calculate the phonon magnetic moment in doped Dirac semimetals, motivated by the recent experimental observation of giant phonon magnetic moment in these materials [1]. Our theory is based on the emergent gauge approach, which can handle both insulators and semimetals, unlike previous theories [2-4]. We show that the phonon magnetic moment is linked to the Hall conductivity through the phonon Hall viscosity. We apply our theory to 2D and 3D Dirac semimetals, such as graphene and Cd3​As2​, and obtain large phonon magnetic moments of the order of electron Bohr magneton using electron-phonon couplings from first-principle calculations. Our theory not only explains the recent experimental findings, but also provides practical guidance for the dynamic generation of large magnetization in materials.

[1] Cheng, B. et al. A Large Effective Phonon Magnetic Moment in a Dirac Semimetal. Nano Lett. 20, 5991–5996 (2020).

[2] Trifunovic, L., Ono, S. & Watanabe, H. Geometric orbital magnetization in adiabatic processes. Phys. Rev. B 100, 054408 (2019).

[3] Ren, Y., Xiao, C., Saparov, D. & Niu, Q. Phonon Magnetic Moment from Electronic Topological Magnetization. Phys. Rev. Lett. 127, 186403 (2021).

[4] Zhang, X.-W., Ren, Y., Wang, C., Cao, T. & Xiao, D. Gate-Tunable Phonon Magnetic Moment in Bilayer Graphene. Phys. Rev. Lett. 130, 226302 (2023).