First-Principles Evidence for Strongly Correlated Superconductivity Driven by Structural Variations in La$_3$Ni$_2$O$_7$

Abstract

We conduct first-principles simulations of La$_3$Ni$_2$O$_7$, a nickelate in which recent experiments have shown signs of high-temperature superconductivity. Within the hydrostatic pressure range where superconductivity is observed, we find a significant increase in effective on-site repulsion in the maximally localised Wannier functions comprising the Ni $e_g$ bands crossing the Fermi energy. We attribute this increase to an interplay between orbital localisation and competing screening channels arising from structural variations. Our results indicate that the superconducting region in the La$_3$Ni$_2$O$_7$ phase diagram coincides with a region of enhanced electronic correlations, which show a close correspondence with the critical temperature. Including finite temperatures up to 100 K, $ab$ $initio$ molecular dynamics simulations then provide new insights into the debated structural phase diagram and further clarify the origin of the right-triangular superconducting dome. Finally, we study Ac$_3$Ni$_2$O$_7$ to confirm the crucial role of the $A$-site cation in shaping the pressure-driven evolution of electronic correlations.

Figures (5)

• Figure 1: Crystal structure and low-energy configuration of La$_3$Ni$_2$O$_7$.a Orthorhombic unit cell of the $Cmcm$ phase, characterized by tilted NiO$_6$ octahedra, shown in gray. b Crystal field splitting and orbital-selective $e_g$ configuration (blue) of two Ni$^{2.5+}$ cations in a dimer. The $d_{z^2}$ orbitals form bonding $d_{z^2,+}$ and anti-bonding $d_{z^2,-}$ states. c Top view of a NiO$_2$ bilayer. Solid and dashed black frames represent the $Fmmm$ and $Cmcm$ unit cells, respectively.
• Figure 2: Enthalpic optimisation of bilayer La$_3$Ni$_2$O$_7$.a Lattice parameters of the orthorhombic unit cell at hydrostatic pressures between 0 and 100 GPa. b The three inequivalent Ni-O-Ni bond angles of the $Cmcm$ phase. The two intralayer angles $\theta_2$ and $\theta_3$ in the $Cmcm$ phase (grey) become equal in the $I4/mmm$ phase (above 10 GPa), and coincidentally the NiO$_6$ octahedra align along the $c$-axis ($\theta_1=180^\circ$).
• Figure 3: Pressure dependence of the band structure and dimer model of La$_3$Ni$_2$O$_7$.a Band structure at 40 GPa, shown as solid lines, with the colour scale indicating the overlap with the different Ni $e_g$ orbitals. The projection onto the spacer La $d_{x^2-y^2}$ orbitals is superimposed as purple circles, with radii representing the weight. The Wannier-interpolated bands obtained from the four maximally localised Wannier functions (MLWFs) are shown as dashed lines. b Band structures at pressures between 20 and 100 GPa. c Pressure dependence of the largest hopping parameters in the dimer model: $\Delta = \epsilon (d_{x^2-y^2}) - \epsilon (d_{z^2})$ is the energy difference between MLWFs, $t^x_{x^2-y^2}$ represents nearest-neighbour intralayer hopping between $d_{x^2-y^2}$ MLWFs and $t^z_{z^2}$ represents interlayer hopping between $d_{z^2}$ MLWFs. d Bare and e screened on-site Coulomb interactions: $V_{x^2-y^2}$ ($U_{x^2-y^2}$) and $V_{z^2}$ ($U_{z^2}$) are the interactions in the $d_{x^2-y^2}$ and $d_{z^2}$ MLWFs as shown in f, while $V_{12}$ ($U_{12}$) denotes the interaction between different on-site MLWFs. g Ratios of screened interaction strengths to their associated hopping parameters and h bare-to-screened interaction ratios.
• Figure 4: AIMD simulations of La$_3$Ni$_2$O$_7$ in the range of 10–100 K and 0–100 GPa. The upper row shows the time-averages of the full diagram, with black dots marking the simulated sampling points. The lower row displays frequency histograms at six pressure-temperature points. Panels (a,b) show the difference between in-plane lattice constants $a$ and $b$, (c,d) the interlayer angle $\theta_1$, and (e,f) the inwards intralayer angle $\theta_2$.
• Figure 5: Pressure-dependent structural and dimer model properties of Ac$_3$Ni$_2$O$_7$ between 0 and 20 GPa.a Lattice constants of the orthorhombic unit cell (as shown for La$_3$Ni$_2$O$_7$ in Fig. \ref{['fig: introduction']}a). b The three unique Ni-O-Ni bond angles of the $Cmcm$ phase. c Hopping parameters and d screened interaction strengths in the dimer model as defined for La$_3$Ni$_2$O$_7$ in Fig. \ref{['fig: electronic']}. Superscripts denote the material: ANO for Ac$_3$Ni$_2$O$_7$ and LNO for La$_3$Ni$_2$O$_7$. e Bare-to-screened interaction ratios and f ratios of screened interaction strengths to their associated hopping parameters.