Nearly Isotropic Vortex Solid in $\mathbf{(La,Pr)_{3}Ni_{2}O_{7}}$ Thin Films

Abstract

The discovery of superconductivity in bulk bilayer nickelates has established a new platform for exploring high-$T_c$ superconductivity beyond the cuprates. The role of the Ni $3d_{z^2}$-derived $\gamma$ band in the superconductivity of bilayer nickelates remains unresolved. By performing simultaneous resistance and diamagnetism measurements on (La,Pr)$_3$Ni$_2$O$_7$ thin films, we map the vortex melting phase diagram for both in-plane and out-of-plane magnetic fields. For $H\parallel c$, the geometric confinement effect gives rise to pancake vortices. Remarkably, the anisotropy parameter of the vortex melting field $\gamma_{H_m} \equiv H_m^{ab}/H_m^c$ decreases monotonically with decreasing temperature and approaches unity at low temperatures. Within the anisotropic Ginzburg--Landau scaling, $H_m^{ab}/H_m^c = \sqrt{\rho_s^{ab}/\rho_s^c}$ tracks the superfluid-density anisotropy. Such a vortex solid implies a nearly isotropic superfluid density, which is irreconcilable with the strictly two-dimensional $3d_{x^2-y^2}$-derived bands, but naturally explained by a substantial interlayer superfluid contribution from the $3d_{z^2}$-derived $\gamma$ band. Our results provide thermodynamic evidence for a substantial contribution of the $\gamma$ band to superconductivity in bilayer nickelate thin films.