Magnus spin Hall and spin Nernst effects in 2D Rashba systems with Zeeman-splitting

We study the Magnus transport in a Zeeman-split 2D electron gas with Rashba spin-orbit coupling using semiclassical Boltzmann transport formalism. The system lies on the $x$-$y$ plane with the bias (electric/thermal) applied along the $x$ direction. Apart from its signature in the charge transport coefficients, the inclusion of Magnus velocity in the spin current operator enables us to study Magnus spin transport in the system. In particular, we study the roles of Zeeman gap and Fermi energy on the behavior of Magnus Hall and Nernst conductivities and their spin counterparts. We find that the Magnus spin Hall conductivity vanishes in the limit of zero Zeeman gap, unlike the universal spin Hall conductivity $\sigma_s=e/(8\pi)$. The Magnus spin conductivities (both for electrically and thermally driven) with polarizations in $\hat{y}$ and $\hat{z}$ directions are finite while that in $\hat{x}$ direction vanishes. Each Magnus conductivity displays a plateau as Fermi energy sweeps through the gap and has peaks (whose magnitudes decrease with the gap) when the Fermi energy is at the gap edges.