Unusual resistive states of multiband superconductors in the effective field theory approach

Starting from the microscopic approach based on multiband Keldysh-Usadel kinetic theory we derive the minimal field-theoretical model equivalent to the time-dependent Ginzburg-Landau theory. We discuss the properties of resistive states determined by the ratio of electric field relaxation length to the superconducting coherence length. In contrast to the well-studied single-band systems we find that this ratio can vary in wide limits in multiband superconductors. As a result, the properties of resistive states in multiband superconductors can be tuned by the microscopic parameters such as the ratio of diffusion coefficients and pairing constants in different bands. As an example we consider moving Abrikosov vortices in two-band superconductor and show that the flux-flow magneto-resistance can strongly deviate from the single-component Bardeen-Stephen estimation in agreement with recent experimental results.