  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.

Mesoscale and Nanoscale Physics