Theory of electric polarization and spin magnetization in inhomogeneous crystals

In this presentation, we derive an expression for electric polarization in inhomogeneous crystals by Kubo formula and discuss the physical meaning. We introduce the inhomogeneity linear in the spatial coordinate and incorporate the perturbation with wavenumber q and frequency ω. By calculating the electric current to the qω order, we obtain an expression for the electric polarization in inhomogeneous crystals. Then, we compare our result with semiclassical theory in Ref. [1], and we discuss the difference between them. Spin magnetization in inhomogeneous crystals is also discussed along the same line, and we can derive the multi-band expression for it, which is consistent with the previous work [2]. If time allows, we demonstrate the validity of our theory by the model calculation.



[1] Y. Zhao, Y. Gao, and D. Xiao, Phys. Rev. B 104, 144023 (2021).

[2] A. Shitade, A. Daido, and Y. Yanase, Phys. Rev. B 99, 024404 (2019).