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Motivated by the recent observation of superconductivity withT_c ~ 80 K in pressurized La₃Ni₂O₇¹, we explore the structural and electronic properties ofA₃Ni₂O₇bilayer nickelates (A = La-Lu, Y, Sc) as a function of pressure (0–150 GPa) from first principles including a Coulomb repulsion term. At ~ 20 GPa, we observe an orthorhombic-to-tetragonal transition in La₃Ni₂O₇at variance with x-ray diffraction data, which points to so-far unresolved complexities at the onset of superconductivity, e.g., charge doping by variations in the oxygen stoichiometry. We compile a structural phase diagram that establishes chemical and external pressure as distinct and counteracting control parameters. We find unexpected correlations betweenT_cand thein-planeNi-O-Ni bond angles for La₃Ni₂O₇. Moreover, two structural phases with significantc⁺octahedral rotations and in-plane bond disproportionations are uncovered forA = Nd-Lu, Y, Sc that exhibit a pressure-driven electronic reconstruction in the Nie_gmanifold. By disentangling the involvement of basal versus apical oxygen states at the Fermi surface, we identify Tb₃Ni₂O₇as an interesting candidate for superconductivity at ambient pressure. These results suggest a profound tunability of the structural and electronic phases in this novel materials class and are key for a fundamental understanding of the superconductivity mechanism.