Electronic structure of Ruddlesden-Popper nickelates: strain to mimic the effects pressure

Signatures of superconductivity under pressure have recently been reported in the bilayer La$_3$Ni$_2$O$_7$ and trilayer La$_4$Ni$_3$O$_{10}$ Ruddlesden-Popper (RP) nickelates with general chemical formula La$_{n+1}$Ni$_n$O$_{3n+1}$ ($n=$ number of perovskite layers along the $c$-axis). The emergence of superconductivity is always concomitant with a structural transition in which the octahedral tilts are suppressed, bringing the apical Ni-O-Ni angle to 180$^\circ$ and causing an increase in the out-of-plane $d_{z^2}$ orbital overlap. Due to this strong interlayer coupling, a flat band of pure $d_{z^2}$ character crosses the Fermi level. Here, using first-principles calculations, we explore biaxial strain (both compressive and tensile) as a means to mimic the electronic structure characteristics of RP nickelates (up to $n=5$) under hydrostatic pressure. Our findings highlight that strain allows to decouple the structural and electronic structure effects obtained under hydrostatic pressure: while compressive strain brings the apical Ni-O-Ni angle closer to 180$^\circ$, it shifts the $d_{z^2}$ flat bands away from the Fermi energy, giving rise to a more cuprate-like electronic structure. In contrast, tensile strain reduces the apical Ni-O-Ni angle (to values $\sim$ 160$^\circ$), but it recovers the flat $d_{z^2}$ band at the Fermi level appearing in the bilayer and trilayer RPs under pressure. Overall, strain represents a promising way to tune the electronic structure of RP nickelates and could be an alternative route to achieve superconductivity at ambient pressure in this family of materials.