Upper Critical Field in Two-Dimensional Superconductors

The upper critical field in two-dimensional superconductors is calculated by taking into account quantum corrections due to the Anderson localization to the theory of dirty superconductors in the order of ( ε F τ 0 ) -1 where ε F and τ 0 are the Fermi energy and the relaxation time of an electron, respectively. The upper critical field is enhanced at low temperatures. This is because the diffusion constant of electrons is depressed and the Coulomb repulsive interaction modified by the localization becomes small in the magnetic field. Discussion is given on the upward curvature of upper critical field of layered superconductors in the field perpendicular to the layers.