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Magnetic penetration depth and $T_c$ in superconducting nickelates

We compute the nominal magnetic penetration depth of $R$NiO$_2$ ($R =$ La, Nd) from first principles calculations and discuss the results in relation to the superconducting $T_c$. We find a marked discrepancy with the well established phenomenology that correlates these two quantities in cuprates (Uemura plot). We also consider the 2D ultrathin limit and estimate the maximum attainable $T_c$ to be $\sim 180$ K according to the Nelson-Kosterliz universal relation between the superfluid density and the transition temperature.