Spin Hall conductivity in topological Dirac semimetals

We theoretically investigate the spin Hall conductivity (SHC) in topological Dirac semimetals (TDSMs) the Dirac points of which are protected by rotational symmetry. On the basis of a general phase diagram of the system with time-reversal, inversion, and fourfold rotational symmetries, we reveal that the SHC is sensitive to the phase to which the system belongs. The phase and the SHC are characterized by the mirror Chern numbers and the presence or absence of gapless bulk Dirac points. It is also found that the representative TDSM Cd3As2 supports a large and negative SHC sigma(z)(xy) similar to -10(4) ((h) over bar /e)(Omega m)(-1). The principle behind the dependency of SHC on the phase diagram is also explained.