Coadjoint-orbit Bosonization for multiband systems in a weak magnetic field – application to the Rashba band and narrow gap insulators

The recently proposed coadjoint orbit bosonization method [1] offers a new theoretical framework for studying gapless fermionic systems at finite density. In this approach, bosonic fields defined in phase space describe fluctuations of the Fermi surface. Notably, it captures the quantum oscillations of magnetization—i.e., the de Haas–van Alphen (dHvA) effect—in two-dimensional Fermi surfaces in a weak magnetic field [2,3]. The problem can be effectively mapped to a single-particle quantum mechanical system with a topological θ-term, which plays a critical role in determining the oscillation period and the phase shift induced by the Berry curvature of the electronic band. In this work, we generalize the bosonization framework to systems with multiple bands near the Fermi surface, where inter-band bosonic fluctuations become significant. We discuss implications for systems with two-fold degenerate bands due to Rashba spin-orbit coupling, as well as for narrow gap insulators.



[1] Luca V. Delacrétaz, Yi-Hsien Du, Umang Mehta, and Dam Thanh Son, Phys. Rev. Research 4, 033131 (2022)



[2] Mengxing Ye and Yuxuan Wang, Phys. Rev. B 112, 035113



[3] Mengxing Ye and Yuxuan Wang, arXiv:2412.16289v2/scipost_202503_00014v1