Classification of spin Hall effect in two-dimensional systems

Abstract

Physical properties such as the conductivity are usually classified according to the symmetry of the underlying system using Neumann’s principle, which gives an upper bound for the number of independent components of the corresponding property tensor. However, for a given Hamiltonian, this global approach usually can not give a definite answer on whether a physical effect such as spin Hall effect (SHE) exists or not. It is found that the parity and types of spin-orbit interactions (SOIs) are good indicators that can further reduce the number of independent components of the spin Hall conductivity for a specific system. In terms of the parity as well as various Rashba-like and Dresselhaus-like SOIs, we propose a local approach to classify SHE in two-dimensional (2D) two-band models, where sufficient conditions for identifying the existence or absence of SHE in all 2D magnetic point groups are presented.

Graphical abstract

Keywords

spin Hall effect / symmetry / two-dimensional system

References

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Declarations

The authors declare that they have no competing interests and there are no conflicts.

Acknowledgements

We acknowledge support from the National Natural Science Foundation of China (Grant Nos. 12034014, 12174262, and 12004442). L. Wang also thanks the Guangdong Basic and Applied Basic Research Foundation (Grant No. 2021B1515130007) and the Shenzhen Natural Science Fund (the Stable Support Plan Program 20220810130956001).

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