Tunable spin-charge conversion in class-I topological Dirac semimetals

We theoretically demonstrate that class-I topological Dirac semimetals (TDSMs) can provide a platform for realizing both electrically and magnetically tunable spin-charge conversion. With time-reversal symmetry, the spin component along the uniaxial rotation axis ($z$-axis) is approximately conserved, which leads to an anisotropic spin Hall effect -- the resulting spin Hall current relies on the relative orientation between the external electric field and the $z$-axis. The application of a magnetic field, on the other hand, breaks time-reversal symmetry, driving the TDSM into a Weyl semimetal phase and, consequently, partially converting the spin current to a charge Hall current. Using the Kubo formulas, we numerically evaluate the spin and charge Hall conductivities based on a low-energy TDSM Hamiltonian together with the Zeeman coupling. Besides the conventional tensor element of the spin Hall conductivity $\sigma_{xy}^z$, we find that unconventional components, such as $\sigma_{xy}^x$ and $\sigma_{xy}^y$, also exist and vary as the magnetic field is rotated. Likewise, the charge Hall conductivity also exhibits appreciable tunability upon variation of the magnetic field. We show that such tunability -- as well as large spin-charge conversion efficiency -- arises from the interplay of symmetry and band topology of the TDSMs.