Upper Critical Field and the Fulde-Ferrel-Larkin-Ovchinnikov Transition in Multiband Superconductors

The effect of orbital and Zeeman pairbreaking on the upper critical field $H_{c2}$ and the Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) transition in clean Fe-based superconductors is addressed using a multiband BCS theory. It is shown that the crystalline anisotropy and the $s^\pm$ pairing symmetry with the sign change of the order parameter on different sheets of the Fermi surface can significantly increase the orbitally-limited $H_{c2}(T)$ and facilitate the FFLO transition. Small pockets of the Fermi surface emerging upon doping can trigger the FFLO transition even for moderate values of the Maki parameter in the main bands.