Symmetry dictionary on charge and spin nonlinear responses for all magnetic point groups with nontrivial topological nature

Zhi-Fan Zhang; Zhen-Gang Zhu; Gang Su

doi:10.1093/nsr/nwad104

Symmetry dictionary on charge and spin nonlinear responses for all magnetic point groups with nontrivial topological nature

Natl Sci Rev. 2023 Apr 27;10(11):nwad104. doi: 10.1093/nsr/nwad104. eCollection 2023 Nov.

Authors

Zhi-Fan Zhang¹, Zhen-Gang Zhu^{1

2

3}, Gang Su^{1

3

4}

Affiliations

¹ School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China.
² School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing 100049, China.
³ CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China.
⁴ Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China.

Abstract

Recently, charge or spin nonlinear transport with nontrivial topological properties in crystal materials has attracted much attention. In this paper, we perform a comprehensive symmetry analysis for all 122 magnetic point groups (MPGs) and provide a useful dictionary for charge and spin nonlinear transport from the Berry curvature dipole, Berry connection polarizability and Drude term with nontrivial topological nature. The results are obtained by conducting a full symmetry investigation of the matrix representations of six nonlinear response tensors. We further identify every MPG that can accommodate two or three of the nonlinear tensors. The present work gives a solid theoretical basis for an overall understanding of the second-order nonlinear responses in realistic materials.

Keywords: magnetic point group; matrix representation; nonlinear response.