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Description
The development of a comprehensive theory capable of fully describing high-temperature superconductors (HTSCs) remains one of the most challenging problems in modern solid-state physics. HTSCs with a superconducting (SC) transition temperature $T_c$ exceeding the boiling point of liquid nitrogen include a well-known class of metal oxides with an active CuO$_{2}$ plane such as YBa$_2$Cu$_3$O$_{7-\delta}$ (or YBCO), commonly referred to as cuprates. These type-II superconductors exhibit a strong $d$-wave anisotropy, low charge carriers density, strong electronic correlations, and quasi-two-dimensionality, as established by numerous studies [1-4].
The high $T_c$-values result in a short size of Cooper pairs, determined by the coherence length. In a crystal lattice, the coherence lengths differ significantly depending on direction: the in-plane coherence length $\xi_{ab}$ is an order of magnitude greater than the out-of-plane coherence length $\xi_{c}$. To determine $\xi_{ab}(T)$ and $\xi_{c}(T)$, it is necessary to measure the temperature dependence of the upper critical field $H_{c_2}(T)$ for magnetic fields applied parallel to both the $ab$-plane and the $c$-axis.
The work provides information about a comparison of the upper critical fields $H_{c_2}(T)$ for optimally doped YBa$_2$Cu$_3$O$_{7-\delta}$ thin films, calculated using Ginzburg-Landau (GL) and Werthamer-Helfand-Hohenberg (WHH) theories. For different magnetic field orientations, WHH theory yields $\mu$$_{0}$$H_{c_2}(0)$ values of $638$ T for $H \parallel ab$ and $153$ T for $H \parallel c$. The GL theory predicts significantly overestimated values, providing, however, a better fit to experimental data.
References
[1] R. Haussmann, “Properties of a Fermi liquid at the superfluid transition in the crossover region between BCS superconductivity and Bose-Einstein condensation,” Physical Review B, vol. 49, no. 18. American Physical Society (APS), pp. 12975–12983, May 01, 1994. https://doi.org/10.1103/physrevb.49.12975
[2] V. M. Loktev et al., “Phase fluctuations and pseudogap phenomena,” Physics Reports, vol. 349, no. 1. Elsevier BV, pp. 1–123, Jul. 2001. https://doi.org/10.1016/s0370-1573(00)00114-9
[3] O. Tchernyshyov, “Noninteracting Cooper pairs inside a pseudogap,” Physical Review B, vol. 56, no. 6. American Physical Society (APS), pp. 3372–3380, Aug. 01, 1997. https://doi.org/10.1103/physrevb.56.3372
[4] J. R. Engelbrecht et al., “Pseudogap above $T_c$ in a model with $d_{x^2-y^2}$ pairing,” Physical Review B, vol. 57, no. 21. American Physical Society (APS), pp. 13406–13409, Jun. 01, 1998. https://doi.org/10.1103/physrevb.57.13406
