Perpendicular Upper Critical Magnetic Field in a Layered d-Wave Superconductor

There exist numerous experimental studies of the perpendicular and parallel upper critical magnetic fields in $d$-wave layered superconductors. They are usually theoretically fitted by the so-called Werthamer, Helfand, and Hohenberg (WHH) results, obtained for an isotropic 3D s-wave superconductors. As theoretically shown by us and by Bulaevskii, layered compounds are characterized by different ratios of the parameter ${{H}_{{c2}}}(0){\text{/}}({\text{|}}d{{H}_{{c2}}}{\text{/}}dT{{{\text{|}}}_{{{{T}_{c}}}}}{{T}_{c}})$, where ${{H}_{{c2}}}(0)$ is the upper critical magnetic field at $T = 0$ and ${\text{|}}d{{H}_{{c2}}}{\text{/}}dT{{{\text{|}}}_{{{{T}_{c}}}}}$ is the so-called Ginzburg–Landau slope near ${{T}_{c}}$. In this paper, we show that for perpendicular upper critical magnetic field of a $d$-wave layered superconductor, the above discussed parameter is equal to ${{H}_{{c2}}}(0){\text{/}}({\text{|}}d{{H}_{{c2}}}{\text{/}}dT{{{\text{|}}}_{{{{T}_{c}}}}}{{T}_{c}}) \approx$ 0.629. To derive this result, we use exact method of the Green’s functions formulation of the BCS microscopic theory of superconductivity by Gor’kov. We compare our results with experimental ones, obtained on the d-wave superconductor YBa₂Cu₃O_{7 – δ}.