Diffusive boundary effect on the superconducting transition temperature of thin films in magnetic field

The diffusive boundary effect on the superconducting transition temperature of a thin film is investigated in the case where the magnetic field is parallel to the film surfaces. In our model, the rough surfaces (the diffusive boundaries) are described by dirty layers, and the scattering effects on the film surfaces are replaced by the impurity scattering in imaginarily contacted dirty layers. The linearized gap equation is analytically derived by a quasi-classical Green's function method, which correctly includes the diffusive boundary effects. It can be shown numerically that the transition temperature is not enhanced by the magnetic field, even in the diffusive boundary condition.