Physics – Condensed Matter – Superconductivity
Scientific paper
2011-12-05
Physics
Condensed Matter
Superconductivity
Scientific paper
The Helfand-Werthamer (HW) scheme 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 literature; it reproduces not only the isotropic HW limit, but the results of calculations for the two-band MgB$_2 along with the existing data on $H_{c2}(T)$ and its anisotropy $\gamma(T)=H_{c2,ab}(T)/H_{c2,c}(T)$ ($a,c$ are 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_za)$, 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_za)$ presumably relevant for pnictides, we obtain $\gamma(T)$ increasing on warming provided both $\eta_1$ and $\eta_2 $ are negative, whereas for $\eta$'s\,$>0$, $\gamma(T)$ decreases. We study the ratio of the two order parameters at $H_{c2}(T)$ and find that the small gap does not vanish at any temperature even at $H_{c2}(T)$, an indication that this does not happen at lower fields.
Kogan Vladimir G.
Prozorov Ruslan
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