We consider the behaviour of the fluctuating specific heat and conductivity in the vicinity of the upper critical field line for a two-band superconductor. Multiple-band effects are pronounced when the bands have very different coherence lengths. The
transition to superconductive state is mainly determined by the properties of the rigid condensate of the strong band, while the weak band with a large coherence length of the Cooper pairs causes the nonlocality in fluctuation behaviour and break down of the simple Ginzburg-Landau picture. As expected, the multiple-band electronic structure does not change the functional forms of dominating divergencies of the fluctuating corrections when the magnetic field approaches the upper critical field. The temperature dependence of the coefficients, however, is modified. The large in-plane coherence length sets the field scale at which the upper critical field has upward curvature. The amplitude of fluctuations and fluctuation width enhances at this field scale due to reduction of the effective z-axis coherence length. We also observe that the apparent transport transition displaces to lower temperatures with respect to the thermodynamic transition. Even though this effect exists already in a single-band case at sufficiently high fields, it may be strongly enhanced in multiband materials.
We explore correlations of inhomogeneous local density of states (LDoS) for impure superconductors with different symmetries of the order parameter (s-wave and d-wave) and different types of scatterers (elastic and magnetic impurities). It turns out
that the LDoS correlation function of superconductor always slowly decreases with distance up to the phase-breaking length $l_{phi}$ and its long-range spatial behavior is determined only by the dimensionality, as in normal metals. On the other hand, the energy dependence of this correlation function is sensitive to symmetry of the order parameter and nature of scatterers. Only in the simplest case of s-wave superconductor with elastic scatterers the inhomogeneous LDoS is directly connected to the corresponding characteristics of normal metal.
