Continuum limit of the upper critical field Hc@f|2 for superconducting networks
Chia-Ren Hu
DOI 10.1103/PhysRevB.35.5294 · Physical Review B
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Abstract
Recently Rammal et al. investigated the upper critical field Hc2* for various superconducting networks and proposed the formula Hc2*= d / 2 Φ0 / πξ2(T) =dHc2(bulk) (with d the spatial dimension of the network) as the universal limiting behavior of Hc2*(T) as T→Tc0,Hc2*→0. We demonstrate with several examples that this is not true for networks with low point-group symmetry. We then propose that the above universal formula be changed to an inequality Hc2*≥2Hc2(bulk), which reduces to an equality for two-dimensional networks with an n-fold rotational symmetry with n≥3. For three dimensional networks Hc2*/Hcs(bulk)=3 if the network has a cubic symmetry. Otherwise we find that the ratio can be larger or smaller than 3.
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