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Based on first-principles calculations including a Coulomb repulsion term, weidentify trends in the electronic reconstruction of $A$NiO$_2$/SrTiO$_3$(001)($A=$ Pr, La) and $A$CuO$_2$/SrTiO$_3$(001) ($A=$ Ca, Sr). Common to all casesis the emergence of a quasi-two-dimensional electron gas (q2DEG) inSrTiO$_3$(001), albeit the higher polarity mismatch at the interface ofnickelates vs. cuprates to the nonpolar SrTiO$_3(001)$ substrate (${3+}/0$ vs.${2+}/0$) results in an enhanced q2DEG carrier density. The simulations reveala significant dependence of the interfacial Ti $3d_{xy}$ band bending on therare-earth ion in the nickelate films, being $20$-$30\%$ larger for PrNiO$_2$and NdNiO$_2$ than for LaNiO$_2$. Contrary to expectations from the formalpolarity mismatch, the electrostatic doping in the films is twice as strong incuprates as in nickelates. We demonstrate that the depletion of the self-dopingrare-earth $5d$ states enhances the similarity of nickelate and cuprate Fermisurfaces in film geometry, reflecting a single hole in the Ni and Cu$3d_{x^2-y^2}$ orbitals. Finally, we show that NdNiO$_2$ films grown on a polarNdGaO$_3(001)$ substrate feature a simultaneous suppression of q2DEG formationas well as Nd~$5d$ self-doping.

Correlated interface electron gas in infinite-layer nickelate versus cuprate films on SrTiO$_3$(001)