  Nickelate superconductors, ${R_{1-x}}{A_x}Ni{O_2}$ (where R is a rare earth
metal and A = Sr, Ca), experimentally discovered in 2019 exhibit many
unexplained mysteries as the existence of a superconducting state with $T_c$ up
to 18 K in thin films and its absence in bulk materials. Another unexplained
mystery of nickelates is their temperature-dependent upper critical field,
$B_{c2}(T)$, which can be nicely fitted to two-dimensional (2D) models; however
the deduced film thickness, $d_{sc,GL}$, exceeds the physical film thickness,
$d_{sc}$, by a manifold. To address the latter, it should be noted that 2D
models assume that $d_{sc}$ is less than the in-plane, $\xi_{ab}(0)$, and
out-of-plane, $\xi_{c}(0)$, ground state coherence lengths, respectively, and,
in addition, that the inequality $\xi_{c}(0) < \xi_{ab}(0)$ satisfies. Analysis
of the reported experimental $B_{c2}(T)$ data showed that at least one of these
conditions does not satisfy for ${R_{1-x}}{A_x}Ni{O_2}$ films. This implies
that nickelate films are not 2D superconductors, even despite though that the
superconducting state is observed only in thin films. Based on this, here we
proposed analytical three dimensional (3D) model for global data fit of
in-plane and out-of-plane $B_{c2}(T)$ in nickelates. The model is based on a
heuristic expression for temperature dependent coherence length anisotropy,
$\gamma_{\xi}(T)$. The proposed expression for $\gamma_{\xi}(T)$, perhaps, has
a much broader application because it has been successfully applied to some
bulk pnictide and chalcogenide superconductors.

Superconductivity