Many-body vortex effect on the transverse force acting on a moving vortex

The nondissipative transverse force acting on one moving vortex under the influence of another vortex is discussed in fermionic superfluid systems, where the relative velocity between the vortices is finite. On the basis of detailed numerical solutions of the Bogoliubov-de Gennes equation, the Berry phase for an adiabatic motion of the vortex line is examined for a two-vortex system. It is found that the detailed electronic structure of a vortex core can affect the transverse force, without abandoning the previous discussions of the robust Magnus force on a single vortex.