Force balance on two-dimensional superconductors with a single moving vortex

We study forces on two-dimensional superconductors with a single moving vortex based on a recent fully self-consistent calculation of DC conductivity in an $s$-wave superconductor (E. Arahata and Y. Kato, arXiv:1310.0566). By considering momentum balance of the whole liquid, we attempt to identify various contributions to the total transverse force on the vortex. This provides an estimation of the effective Magnus force based on the quasiclassical theory generalized by Kita [T. Kita, Phys. Rev. B, {\bf 64}, 054503 (2001)], which allows for the Hall effect in vortex states.