Effects of grain boundaries on microwave surface resistance of superconducting films

Microwave surface resistance of superconducting films with grain boundaries (GBs) is theoretically investigated as the functions of the critical current density J_cj at GB junctions and of the film thickness d. The two-fluid model is used for electrical current in the grains, whereas the Josephson-junction model is adopted for tunneling current across GBs. Theoretical expressions of the surface resistance R_sf are obtained not only for weakly coupled GBs with small J_cj but also for strongly coupled GBs with large J_cj. The results show that R_sf nonmonotonically depends on the critical current density J_cj at GB junctions, and R_sf of superconductors with GBs can be smaller than the surface resistance for ideal homogeneous superconductors without GB. The R_sf is proportional to 1/d for thin films of d≪d_cr and R_sf is independent of d for thick slabs of d≫d_cr, where the crossover thickness d_cr is much larger than 2λ (where λ is the London penetration depth) for weakly coupled GBs.