Abstract
Nickelate superconductors, R(1-x)A(x)NiO(2) (where R is a rare earth metal and A = Sr, Ca), experimentally discovered in 2019, exhibit many unexplained mysteries, such as the existence of a superconducting state with T(c) (up to 18 K) in thin films and yet absent in bulk materials. Another unexplained mystery of nickelates is their temperature-dependent upper critical field, Bc2(T), which can be nicely fitted to two-dimensional (2D) models; however, the deduced film thickness, dsc,GL, exceeds the physical film thickness, dsc, by a manifold. To address the latter, it should be noted that 2D models assume that dsc is less than the in-plane and out-of-plane ground-state coherence lengths, dsc<ξab(0) and dsc<ξc(0), respectively, and, in addition, that the inequality ξc(0)<ξab(0) satisfies. Analysis of the reported experimental Bc2(T) data showed that at least one of these conditions does not satisfy for R(1-x)A(x)NiO(2) films. This implies that nickelate films are not 2D superconductors, despite the superconducting state being observed only in thin films. Based on this, here we propose an analytical three-dimensional (3D) model for a global data fit of in-plane and out-of-plane Bc2(T) in nickelates. The model is based on a heuristic expression for temperature-dependent coherence length anisotropy: γξ(T)=γξ(0)1-1a×TTc, where a>1 is a unitless free-fitting parameter. The proposed expression for γξ(T), perhaps, has a much broader application because it has been successfully applied to bulk pnictide and chalcogenide superconductors.