Quantum theory of orbital magnetic quadrupole moment with the Chern-Simons term

ORAL

Abstract

Recently, the quantum formula of orbital magnetic quadrupole moments, defined as a response to the spatial modulation of magnetic fields, was derived [1,2]. Here, the derivative of the magnetic quadrupole moments with respect to the chemical potential is expected to be equal to the orbital magnetoelectric tensor, but the previous research do not satisfy this property. In this work, by considering a response to the spatial modulation of magnetic fields including a monopole field, we derive a modified formula for the magnetic quadrupole moment, whose derivative correctly reproduces the orbital magnetoelectric effect. In particular, we show that the trace of the magnetic quadrupole moment comes from the correction of density of states due to the monopole field, and it has the Chern-Simons axion term as expected. We also discuss that the magnetic quadrupole moment derived as such is not equal to the classicaliy defined quadrupole moment, but it has additional terms.

[1] A. Shitade, H. Watanabe, and Y. Yanase, Phys. Rev. B 98, 020407(R) (2018).

[2] Y. Gao and D. Xiao, Phys. Rev. B 98, 060402(R) (2018).

*This work was supported by JST SPRING, Grant Number JPMJSP2106 and JSPS KAKENHI Grant Number JP22H00108.N.A. also acknowledges the financial support from Advanced Research Center for Quantum Physics and Nanoscience, Tokyo Institute of Technology.Y.G. acknowledges the support of the 363 Fundamental Research Funds for the Central Universities, 364 China(Grant No. WK2340000102).D.X. is supported by DOE Award No. DE-SC0012509.

–

Presenters

  • Nobuhiro Arai

    • Department of Physics, Tokyo Institute of Technology

Authors

  • Nobuhiro Arai

    • Department of Physics, Tokyo Institute of Technology

  • Yang Gao

    • University of Science and Technology of China, Hefei, Anhui 230026, China

  • Di Xiao

    • University of Washington
    • 1. Department of Materials Science & Engineering, University of Washington, Seattle WA 98915 2. Department of Physics, University of Washington, Seattle WA 98915
    • Department of Materials Science & Engineering, Department of Physics, University of Washington; Pacific Northwest National Laboratory

  • Shuichi Murakami

    • Tokyo Institute of Technology, Tokyo
    • Department of Physics, Tokyo Institute of Technology