This paper deals with the theory of the density of states of pure type-II superconductors in high magnetic fields. An approximate expression of the GaEEN'S function is derived by using the fact that it has the periodicity of the lattice of flux lines in the center-ofmass coordinates. In comparison to the normal state GREEN'S function a correction term proportional to the absolute square of the order parameter arises. This is seen to act as a self-energy part depending strongly on the polar angle O of the "quasiparticle" momentum relative to the direction of the field. The corresponding density of states, as a function of the excitation energy, is found to vary from the gapless to the BCS type as the parameter O changes from u]2 to zero (or u). The averaged state density varies gradually from a uniform to a BCS-like state density as the external field decreases sufficiently far below the upper critical field. The results of the present theory for the averaged density of states agree fairly well with the results due to a conjecture by MAKI if the field is very close to the upper critical field.
I. IntroductionSeveral attempts have been made to calculate the space average of the density of states, N(co), in a type-II superconductor in the high magnetic field region by means of a perturbation expansion in powers of the order parameter, A (r). For a pure type-II superconductor it was found first by DE GENNES et al. 1 that N(co) has a logarithmic singularity at zero excitation energy co (where co is measured relatively to the chemical potential). Later the density of states was calculated exactly by NEU-MANN z to order ]A 12 (the bar denotes the spatial average) for all mean free paths of the electrons. It turns out that for finite mean free paths, no matter how large, the singularity disappears. Then the shape of the curve of N(co) versus co becomes qualitatively similar to that of the dirty limit 3, in particular it shows no energy gap.Recently it was shown by MAKI 4 that for pure type-II superconductors the contribution to N(co) of the order ]AI ~ diverges even stronger than that of the order [A [2, namely, it goes like 1/co 2 as co tends to zero.
We have calculated within the fluctuation exchange approximation the full momentum and realfrequency dependence of the quasiparticle self-energy, the gap function, and the dynamic spin suscepti-
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