The minimal magnetic field $H_{ c2}$ destroying superconductivity in the { \it bulk} of a superconductor is smaller than the magnetic field $H_{ c3}$ needed to destroy { \it surface} superconductivity if the surface of the superconductor coincides with one of the crystallographic planes and is parallel to the external magnetic field. While for a dirty single-band superconductor the ratio of $H_{ c3}$ to $H_{ c2}$ is a universal temperature-independent constant 1.6946, for dirty two-band superconductors this is not the case. I show that in the latter case the interaction of the two bands leads to a novel scenario with the ratio $H_{ c3}/H_{ c2}$ varying with temperature and taking values larger and smaller than 1.6946. The results are applied to ${ \rm MgB}_2$ and are in agreement with recent experiments [A. Rydh { \it et al.}, cond-mat/0307445].
Categories: cond-mat.supr-con cond-mat.dis-nn cond-mat.mtrl-sci