The upper critical field H c2 is evaluated for weakly-coupled two-band anisotropic superconductors. By modeling the actual bands and the gap distribution of MgB 2 by two Fermi surface spheroids with average parameters of the real material, we show that H c2;ab =H c2;c increases with decreasing temperature in agreement with available data.The anisotropic Ginzburg-Landau (GL) equations, derived for clean superconductors with arbitrary gap anisotropy by Gor'kov and Melik-Barkhudarov, 1) led to a common practice of characterizing materials by a single anisotropy parameter defined as a = c c = a ( is the coherence length, is the penetration depth, and a; c are principal directions of a uniaxial crystal of the interest here). Formally, this came out because in the GL domain, the same ''mass tensor'' determines the anisotropy of both (of the upper critical fields H c2 ) and of .At arbitrary temperatures, however, the ratios of H c2 's and of 's are not necessarily the same. We demonstrate below that in materials with anisotropic Fermi surfaces and anisotropic gaps, not only H c2;a =H c2;c may strongly depend on T, but this ratio might differ considerably from c = a at low T's. Our arguments are based on the weak-coupling model of superconductivity for simple Fermi surfaces and gap anisotropies; as such they are at best qualitative. Still, being applied to MgB 2 , they provide satisfactory description of existing data for the H c2 anisotropy.There are two different approaches in literature in describing macroscopics of the ''two-gap'' superconductivity of MgB 2 . One of these treats the anisotropy of interaction by introducing a coupling matrix ij for intra-and interband pair transfer. Various relations between the matrix elements yield variety of macroscopic consequences. One of the realizations of the model considers two order parameters with two distinct phases which may lead to various static 2,3) and dynamic 4) effects. Certain relations between elements ij provide the experimentally observed gaps and their ratio. The approach adopted in this paper considers the gap on two Fermi sheets just as a particular case of the gap anisotropy, the gap ratio being the experimental input parameter. Within this scheme, there is only one complex order parameter É, a single critical temperature T c is built in, and the number of input parameters needed for calculations is small. The resulting H c2 's of these two approaches are similar. 5) Our choice is dictated by theoretical simplicity, rather than by experimental necessity.Below, the general scheme of calculating H c2 ðTÞ based on the Eilenberger method 6) is outlined for both the gap and the Fermi surface being anisotropic. 7) Then, we estimate the H c2 anisotropy of MgB 2 by modeling the four-sheet Fermi surface as calculated in refs. 8-10, by two distinct Fermi sheets F 1;2 with gaps Á 1;2 , each being constant within its sheet. Since the actual band structure enters macroscopic superconducting parameters via Fermi-surface averages, we further model the sheets F 1;2 by two s...

The physics behind the rhombic-->square-->rhombic flux line lattice transformation in increasing fields is clarified on the basis of Eilenberger theory. We demonstrate that this reentrance observed in LuNi2B2C is due to intrinsic competition between the superconducting gap and Fermi surface anisotropies. The calculations not only reproduce it but also predict the not yet found lock-in transition to a square lattice with different orientation in a higher field. In view of the physical origin given, this sequence of transitions is rather generic to occur in fourfold symmetric superconductors.

Orientational field-dependence of the zero energy density of states (ZEDOS) is calculated for superconductors with the polar state (line node), axial state (point node) and 3D d-wave state. Depending on the gap topology and relative field direction the field dependencies of ZEDOS sensitively differ, providing us a useful and practical method to identify the gap topology. It is also demonstrated that for d-wave state the field rotation in the basal plane shows a sizable oscillation (∼3%) of ZEDOS. This is directly measurable in low-T specific heat experiment in the mixed state.

To identify the superconducting gap structure in URu2Si2, we perform field-angle-dependent specific heat measurements for the two principal orientations in addition to field rotations, and a theoretical analysis based on microscopic calculations. The Sommerfeld coefficient gamma(H)'s in the mixed state exhibit a distinctly different field dependence. This comes from point nodes and the substantial Pauli paramagnetic effect of URu2Si2. These two features combined give rise to a consistent picture of superconducting properties, including a possible first order transition of Hc2 at low temperatures.

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