Beyond the standard model of Ginzburg–Landau theory: multiband superconductors

The recently discovered multiband superconductors have created a new class of novel superconductors. In these materials multiple superconducting gaps arise due to the formation of Cooper pairs on different sheets of the Fermi surfaces. An important feature of these superconductors is the interband couplings, which not only change the individual gap properties, but also create new collective modes. Here we investigate the effect of the interband couplings in the Ginzburg–Landau theory. We produce a general τ(2n + 1)/2 expansion (τ = 1 − T/Tc) and show that this expansion has unexpected behaviour for n ⩾ 2. This point emphasises the weaker validity of the GL theory for lower temperatures and gives credence to the existence of hidden criticality near the critical temperature of the uncoupled subdominant band. We apply this theory to a range of material parameters fitted to experimental measurements and find that for some cases the theory performs very well at all temperatures, but for other materials the range of applicability can be very limited. (paper)