Orbital upper critical field and its anisotropy of clean one- and two-band superconductors

TitleOrbital upper critical field and its anisotropy of clean one- and two-band superconductors
Publication TypeJournal Article
Year of Publication2012
AuthorsKogan VG, Prozorov R
Journal TitleReports on Progress in Physics
Volume75
Pages114502
Date Published11
Type of ArticleReview
ISBN Number0034-4885
Accession NumberWOS:000310454300003
Keywordsdependence, equations, mgb2, parameters, single-crystals, temperature
Abstract

The Helfand-Werthamer (HW) scheme (Helfand and Werthamer 1966 Phys. Rev. 147 288; another part of this work published as a separate paper by Werthamer et al 1966 Phys. Rev. 147 295) of evaluating the orbital upper critical field is generalized to anisotropic superconductors in general, and to two-band clean materials, in particular. Our formal procedure differs from those in the literature; it reproduces not only the isotropic HW limit but also the results of calculations for the two-band superconducting MgB2 (Miranovic et al 2003 J. Phys. Soc. Japan 72 221, Dahm and Schopohl 2003 Phys. Rev. Lett. 91 017001) along with the existing data on H-c2(T) and its anisotropy gamma(T) = H-c2,H-ab(T)/H-c2,H-c(T) (a, c are the principal directions of a uniaxial crystal). Using rotational ellipsoids as model Fermi surfaces we apply the formalism developed to study gamma(T) for a few different anisotropies of the Fermi surface and of the order parameters. We find that even for a single band d-wave order parameter gamma(T) decreases on warming; however, relatively weakly. For order parameters of the form Delta(k(z)) = Delta(0)(1 + eta cos k(z)a) (Xu et al 2011 Nature Phys. 7 198), according to our simulations gamma(T) may either increase or decrease on warming even for a single band depending on the sign of eta. Hence, the common belief that the multi-band Fermi surface is responsible for the temperature variation of gamma is proven incorrect. For two s-wave gaps, gamma decreases on warming for all Fermi shapes examined. For two order parameters of the form Delta(k(z)) = Delta(0)(1 + eta cos k(z)a), presumably relevant for pnictides, we obtain gamma(T) increasing on warming provided both eta(1) and eta(2) are negative, whereas for eta > 0, gamma(T) decreases. We study the ratio of the two order parameters at H-c2(T) and find that the ratio of the small gap to the large one does not vanish at any temperature, even at H-c2(T), an indication that this does not happen at lower fields.

URL<Go to ISI>://WOS:000310454300003
DOI10.1088/0034-4885/75/11/114502
Alternate JournalRep. Prog. Phys.