Bilayer Two-Orbital Model of $\mathrm{L}{\mathrm{a}}_3\mathrm{N}{\mathrm{i}}_2{\mathrm{O}}_7$ under Pressure

The newly discovered Ruddlesden-Popper bilayer ${\mathrm{La}}_3{\text{Ni}}_2{\mathrm{O}}_7$ reaches a remarkable superconducting transition temperature $T_c\approx 80\mathrm{K}$ under a pressure of above 14 GPa. Here we propose a minimal bilayer two-orbital model of the high-pressure phase of ${\mathrm{La}}_3{\text{Ni}}_2{\mathrm{O}}_7$. Our model is constructed with the Ni-$3d_{x^2-y^2}$, $3d_{3z^2-r^2}$ orbitals by using Wannier downfolding of the density functional theory calculations, which captures the key ingredients of the material, such as band structure and Fermi surface topology. There are two electron pockets, $\alpha$, $\beta$, and one hole pocket, $\gamma$, on the Fermi surface, in which the $\alpha$, $\beta$ pockets show mixing of two orbitals, while the $\gamma$ pocket is associated with $\mathrm{Ni}\text{−}{d}_{3z^2-r^2}$ orbital. The random phase approximation spin susceptibility reveals a magnetic enhancement associated with the $d_{3z^2-r^2}$ state. A higher energy model with $\mathrm{O}\text{−}p$ orbitals is also provided for further study.

Figure 1

The DFT band structure and partial density of states of the high-pressure Fmmm phase of ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$. The blue, red, and green colors represent $\mathrm{Ni}\text{−}{d}_{x^2-y^2}$, $d_{3z^2-r^2}$, and $\mathrm{O}\text{−}p$ states, respectively.

Figure 2

Schematic of the bilayer ${\mathrm{La}}_3{\text{Ni}}_2{\mathrm{O}}_7$ lattice with hopping parameters. (a) Only $\mathrm{Ni}\text{−}{d}_{x^2-y^2}$ (red), $d_{3z^2-r^2}$ (blue) orbitals are shown. The blue, red, and green lines indicate hoppings for the bilayer two-orbital model. Their values are listed in Table 1. (b) Extra $\mathrm{O}\text{−}p$ orbitals are drawn as green shapes, with in-plane $p_x$, $p_y$ and apical $p_z,p_z^{\prime },p_z^{\prime \prime }$. Some of the $p_z^{\prime },p_z^{\prime \prime }$ are hidden for clarity. The hopping parameters are given in Table 2.

Figure 3

The band structure (a) and Fermi surface (b) of the bilayer two-orbital model. The color bar indicates the orbital weight of $d_{x^2-y^2}$ and $d_{3z^2-r^2}$.

Figure 4

Spin susceptibility ${\chi }_S^{st,\mathrm{RPA}}(q,\omega =0)$ of the bilayer two-orbital model. (a) The total orbital sum ${\chi }_S^{\mathrm{RPA}}={\sum }_{st}{\chi }_S^{st,\mathrm{RPA}}$ which corresponds to the experimental measurable. [(b)–(d)] Orbital-resolved ${\chi }^{st,\mathrm{RPA}}$. An amplified factor of 2 is used in (b) and (c).