%0 Journal Article
%J Reports on Progress in Physics
%D 2012
%T Orbital upper critical field and its anisotropy of clean one- and two-band superconductors
%A Kogan, V. G.
%A Prozorov, R.
%K dependence
%K equations
%K mgb2
%K parameters
%K single-crystals
%K temperature
%M WOS:000310454300003
%P 114502
%R 10.1088/0034-4885/75/11/114502
%U ://WOS:000310454300003
%V 75
%X 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.
%Z ISI Document Delivery No.: 028WCTimes Cited: 0Cited Reference Count: 50Kogan, V. G. Prozorov, R.Department of Energy - Basic Energy Sciences [DE-AC02-07CH11358]Some ideas described in this text were conceived in discussions with Predrag Miranovich while working on Hc2(T) of MgB2 in 2002; VK is grateful to Predrag for this experience. We thank Andrey Chubukov for turning our attention to order parameters of the form (104) and our Ames Lab colleagues John Clem, Andreas Kreyssig, Sergey Bud'ko, Makariy Tanatar and Paul Canfield for interest and critique. We are grateful to Erick Blomberg for reading the manuscript and useful remarks. Work at the Ames Laboratory is supported by the Department of Energy - Basic Energy Sciences under Contract No DE-AC02-07CH11358.Iop publishing ltdBristol
%8 11
%9 Review
%@ 0034-4885