Leggett modes and vortex dynamics in time-reversal symmetry breaking multiband superconductors

In the framework of quasiclassical kinetic theory we study the spectrum of collective excitations and vortex dynamics in multiband superconductors. We show that the existence of mixed phase-density modes in multiband superconductors with broken time-reversal symmetry generates a new contribution to the viscosity of magnetic flux flow. Near the time reversal symmetry breaking phase transition this new contribution dominates over the usual Tinkham and Bardeen-Stephen mechanisms and provides a peculiar temperature dependence of the vortex viscosity. The results could be relevant for three band superconductor Ba$_{\mathrm{1-x}}$K$_{\mathrm{x}}$Fe$_{\mathrm{2}}$As$_{\mathrm{2}}$.