Upper critical field for anisotropic superconductivity: A tight-binding approach

Abstract

We study the problem of the upper critical field (Hc2) for tight-binding electrons in a two-dimensional lattice. The external magnetic field is introduced into the model Hamiltonian both via the Peierls substitution and the Zeeman term. Carrying out calculations for finite systems we analyze the influence of the external field in the commensurable and incommensurable case on an equal footing. The upper critical field has been investigated for intrasite as well as anisotropic intersite pairing that, in the absence of magnetic field, has a dx2−y2 symmetry. We also briefly discuss the symmetry of the superconducting order parameter in the presence of magnetic field and the role of the next-nearest-neighbor hopping. A comparison of Hc2 determined for different symmetries shows that for nested Fermi surface the on-site pairing is more affected by the external field, i.e., the critical temperature for the on-site pairing decreases with the increase of the magnetic field faster than in the anisotropic case. Moreover, we have shown that the tight-binding form of the Bloch energy can lead to the upward curvature of Hc2, provided that the Fermi level is close enough to the van Hove singularity.

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