Structural routes to stabilize superconducting ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ at ambient pressure

The bilayer perovskite ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ has recently been found to enter a superconducting state under hydrostatic pressure at temperatures as high as 80 K. The onset of superconductivity is observed concurrent with a structural transition which suggests that superconductivity is inherently related to this specific structure. Here we perform density functional theory based structural relaxation calculations and identify several promising routes to stabilize the crystal structure which hosts the superconducting state at ambient pressure. We find that the structural transition is controlled almost entirely by a reduction of the $b$-axis lattice constant, which suggests that uniaxial compression along the [010] direction or in-plane biaxial compression are sufficient as tuning parameters to control this transition. Furthermore, we show that increasing the size of the $A$-site cations can also induce the structural transitions via chemical pressure and identify ${\mathrm{Ac}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ and Ba-doped ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ as potential candidates for a high temperature superconducting nickelate at ambient pressure.

Figure 1

(a), (b) Crystal structure of ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ with Ni (blue), oxygen (yellow) in space group $Amam$ (a) and $Fmmm$ (b). (c) Comparison of the Ni-O-Ni bond angle parallel to the $c$ axis (red, ${\theta }_c$) and $ab$ plane (blue, ${\theta }_{ab}$) as a function of hydrostatic pressure (percentage reduction of the $a,b,c$ lattice constants) from DFT relaxation simulations. The in-plane Ni-O-Ni bond angle evolves from concave to convex as pressure is increased (lattice constants reduced) with an inflection point at 3%. (d) Low energy band structure of ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ with $Amam$ symmetry from the relaxed structure at 0% pressure and (e) the $Fmmm$ band structure from the relaxed structure at 4% pressure. corresponding to approximately 24 GPa hydrostatic pressure. (e) The bands are plotted along the high symmetry $\mathbf{k}$ path $\mathrm{\Gamma }=(0,0,0)$, $M=(\pi ,\pi ,0)$, $X=(\pi ,0,0)$, $Z=(0,0,\pi )$, $A=(\pi ,\pi ,\pi )$, and $R=(\pi ,0,\pi )$. Purple and yellow coloring correspond to $d_{z^2}$ and $d_{x^2-y^2}$ dominant orbital character, respectively; other colors represent the $t_{2g}$ orbitals.

Figure 2

Effect of biaxial and uniaxial strain ($\epsilon$) on the structural transition of ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$. Evolution of the in-plane and out-of-plane Ni-O-Ni bond angles as a function of (a) biaxial strain along [100] and [010]. (b) Uniaxial strain along $c$. (c) Uniaxial strain along the [010] (solid lines) and [100] (dashed lines) directions, ${45}^{\circ }$ to the Ni-Ni direction. (d) Uniaxial strain along the [110] direction (Ni-Ni direction). Note that this breaks the symmetry of the Ni-O-Ni bonds along the [110] and [$1-10]$ directions so both are plotted. The light blue color indicates the $Fmmm$ lattice symmetry. An inset of the strain with relation to the crystal structure has been included in (a), with the La, Ni, and O atoms colored as gray, blue, and yellow, respectively.

Figure 3

Influence of the $A$-site cation on the structure of ${\mathrm{A}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$. (a) Relaxed structure of ${\mathrm{A}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ for six different $A$-site cations, $A=\text{Ce,}\text{La,}\text{Ac,}\text{Ba,}\text{Sr,}\text{Ca}$. The out-of-plane and in-plane Ni-O-Ni bond angles (${\theta }_c$ and ${\theta }_{ab}$, respectively) are also shown. The corresponding band structures within $500\mathrm{meV}$ of the Fermi level are shown in (b)–(e) for (b) ${\mathrm{Ac}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$, (c) ${\mathrm{Ce}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$, (d) ${\mathrm{Ba}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$, and (e) ${\mathrm{Sr}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$. Red, green, and blue lines correspond to bands with $\mathrm{Ni}3d_{xz}$, $3d_{yz}$, and $3d_{xy}$ orbital character, whereas yellow and purple correspond to the $3d_{x^2-y^2}$ and $3d_{z^2}$ orbitals, respectively. The black bands in (c) are $4f$-derived bands from the $\mathrm{Ce}$ atom.

Figure 4

Comparison of the Ni-O-Ni bond angle for (a) hydrostatic pressure, (b) biaxial strain, and (c) uniaxial strain along the [010] or $b$ axis. Obtained from structural relaxations using $\mathrm{DFT}+U$ with $U=3\mathrm{eV}$ applied to the Ni site. These are equivalent calculations to the $U=0\mathrm{eV}$ calculations performed in Fig. 1, Fig. 2, and Fig. 2 of the main text, respectively. The pressure axis was determined from the trace of the stress tensor obtained for the relaxed calculations.

Figure 5

Calculated phonon dispersion for the DFT relaxed crystals of (a) ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$, (b) ${\mathrm{Ac}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$, and (c) ${\mathrm{Ba}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$.

Figure 6

Structural modifications of the octahedral rotation angles for the surface and subsurface layer of ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$. Due to the lack of inversion symmetry, there is now a distinction between the upper and lower Ni-O-Ni bond parallel to the $ab$ plane. These are defined as ${\theta }_{ab}^t$ and ${\theta }_{ab}^b$ for the top and bottom Ni-O-Ni layers, respectively.