Upper critical field and the Fulde-Ferrel-Larkin-Ovchinnikov transition in multiband superconductors

The effect of orbital and Zeeman pair breaking on the upper critical field Hc2 and the Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) transition in clean anisotropic multiband superconductors is addressed. For a uniaxial superconductor with a single parabolic band, a close form equation for Hc2(T,θ) as functions of temperature T and the angle θ between H and the c axis is obtained. The wave vector Q of the FFLO oscillations is shown to be not parallel to the magnetic field H if it is tilted away from the symmetry axis. For multiband superconductors, the crystalline anisotropy, and the s^± pairing symmetry with the sign change of the order parameter on different sheets of the Fermi surface can significantly increase the orbitally limited Hc2 and facilitate the FFLO transition. It is shown that if shadow bands exist close to the Fermi level (as characteristic of ferropnictides), a small shift of the chemical potential upon doping can trigger the FFLO transition produced by emerging small pockets of the Fermi surface even for moderate values of the Maki parameter in the main bands.