Two-dimensional superconductivity of epitaxial tantalum films

The recently realized single crystalline $\ensuremath{\alpha}$-phase tantalum (Ta) films, mainly explored for their use in quantum computing, are yet another elemental superconductor with strong spin-orbit interactions. In this work, we address the superconducting properties of the $\ensuremath{\alpha}$-Ta films from the two-dimensional (2D) limit to the 2D-3D crossover regime. We epitaxially grow $\ensuremath{\alpha}$-Ta thin films with thicknesses ranging from 6.5 nm to over 160 nm on ${\mathrm{Al}}_{2}{\mathrm{O}}_{3}$ substrates. Interestingly, the in-plane upper critical magnetic fields ${B}_{c2,\ensuremath{\parallel}}$ of our Ta films always exhibit a parabolic temperature dependence---one defining character of 2D superconductivity. The extracted superconducting thickness ${d}_{\mathrm{sc}}$ can reach 1.7--2.4 times the in-plane coherence length ${\ensuremath{\xi}}_{ab}$ in the relatively thick films (90--160 nm), drawing a sharp contrast to the usual expectation of ${d}_{\mathrm{sc}}<{\ensuremath{\xi}}_{ab}$ for 2D superconductors. Furthermore, we observe deviation from the 2D Tinkham behavior in the angular dependence of the upper-critical field only in the thickest sample (about 160 nm). It suggests that Ta enters the 2D-3D crossover regime at a very large sample thickness. Finally, we analyze the enhancement of ${B}_{c2,\ensuremath{\parallel}}$ over the Pauli limit in the thinnest sample. The systematic evolution of ${B}_{c2,\ensuremath{\parallel}}$ as a function of thickness suggests the involvement of intrinsic spin-orbit interactions.