2018/06/22 by Satoru Hayami, Megumi Yatsushiro, Yuki Yanagi +1 · 3 citations
Physics and Astronomy · #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.98.165110
published as Phys. Rev. B 98, 165110 (2018) · 37 pages, 4 figures, 32 tables
arxiv created 2018/06/22 · arxiv updated 2018/10/24
Four types of atomic-scale multipoles, electric, magnetic, magnetic toroidal, and electric toroidal multipoles, give a complete set to describe arbitrary degrees of freedom for coupled charge, spin, and orbital of electrons. We here present a systematic classification of these multipole degrees of freedom towards the application in condensed matter physics. Starting from the multipole description under the rotation group in real space, we generalize the concept of multipoles in momentum space with the spin degree of freedom. We show how multipoles affect the electronic band structures and linear responses, such as the magneto-electric effect, magneto-current (magneto-gyrotropic) effect, spin conductivity, Piezo-electric effect, and so on. Moreover, we exhibit a complete table to represent the active multipoles under 32 crystallographic point groups. Our comprehensive and systematic analyses will give a foundation to identify enigmatic electronic order parameters and a guide to evaluate peculiar cross-correlated phenomena in condensed matter physics from microscopic point of view.