Theory of the upper critical field in layered superconductors

The upper critical field $H_{c2}$ in layered superconductors is calculated from a microscopic theory in which the electrons are assumed to propagate freely within the individual layers subject to scattering off impurities and to propagate via tunneling between the layers. For the magnetic field parallel to the layers, there is a temperature $T^{*}<T_c$ below which the normal cores of the vortices fit between the metallic layers, removing the orbital effects as a mechanism for the quenching of superconductivity in the individual layers. In this temperature regime, $H_{c2\parallel }$ is thus determined by the combined effects of Pauli paramagnetism and spin-orbit scattering, and for sufficiently strong spin-orbit scattering rates, $H_{c2\parallel }\mathrm{}(T=0\mathrm{})\mathrm{}$ can greatly exceed the Chandrasekhar-Clogston Pauli limiting field $H_P$. This unusual behavior is found to be most pronounced in the dirty limit for the electron propagation within the layers and when the electrons scatter many times in a given layer before tunneling to an adjacent layer. Our results are also discussed in light of the available experimental data.