Electronic Structure, Magnetic and Pairing Tendencies of Alternating Single-layer Bilayer Stacking Nickelate La$_5$Ni$_3$O$_{11}$ Under Pressure

Abstract

Nickelates have continued to surprise since their unconventional superconductivity was discovered. Recently, the layered nickelate La$_5$Ni$_3$O$_{11}$ with hybrid single-layer and bilayer stacking showed superconductivity under high pressure. This compound combines features of La$_2$NiO$_4$ and La$_3$Ni$_2$O$_7$, but its pairing mechanism remains to be understood. Motivated by this finding, here we report a comprehensive theoretical study of this system. Our density functional theory calculations reveal that the undistorted P4/mmm phase without pressure is unstable due to three distortion modes. Increasing pressure suppresses these modes and causes ``charge transfer'' between the single-layer and bilayer sublattices, leading to hole-doping in the single-layer blocks. Our random-phase approximation calculations indicate a leading $d_{x^2-y^2}$-wave pairing state that arises from spin-fluctuation scattering between Fermi surface states mainly originating from the single-layer blocks and additional weaker contributions from the bilayer blocks. These spin-fluctuations could be detected by inelastic neutron scattering as a strong peak at ${\bf q}=(π, π)$. Our findings distinguish La$_5$Ni$_3$O$_{11}$ from other nickelate superconductors discovered so far and the high-$T_c$ cuprates. We also discuss both similarities and differences between La$_5$Ni$_3$O$_{11}$ and other hybrid stacking nickelates.

Figures (7)

• Figure 1: Comparison between RP nickelate La$_{n+1}$Ni$_n$O$_{3n+1}$ and 1212-LNO.a BL Ni lattice and the sketch of the Fermi surface of La$_3$Ni$_2$O$_7$, which superconducts under pressure. As shown in the right panel, an $s_{\pm}$-wave channel is favored due to the nesting vector ${\bf q}=(\pi, 0)/(0, \pi)$ connecting the M = $(\pi, \pi)$ centered pockets and portions of the Fermi surface centered at the X = $(\pi, 0)$ [or Y = $(0, \pi)$] points. b SL Ni lattice and the sketch of the Fermi surface of La$_2$NiO$_4$, which does not superconduct at both ambient and high-pressure condition. c SL BL stacking Ni superlattice and the sketch of the Fermi surface of 1212-LNO, which superconducts under pressure. In contrast to the BL nickelate, a $d_{x^2-y^2}$-wave channel is favored due to the nesting vector ${\bf q}=(\pi, \pi)$ connecting the M = $(\pi, \pi)$ centered sheets and portions of the Fermi surface centered at the $\Gamma$ sheets, as shown in the right panel.
• Figure 2: Crystal structure and phonon spectrum.a Schematic crystal structures of conventional P4/mmm (No. 123) and Cmmm (No. 65) phases of 1212-LNO (green = La; blue = Ni; red = O). All crystal structures were visualized using the VESTA code Momma:vesta. b, c Phonon spectrum of the P4/mmm (No. 123) phase of 1212-LNO at 0 GPa, and at 10 GPa, respectively. The results at other pressures can be found in Supplementary Note II.
• Figure 3: Group theory analysis, distortion amplitudes, and phase transition.a The group theory analysis for 1212-LNO is based on the unstable phonon modes for the P4/mmm phase at 0 GPa and the schematic crystal structures led by those modes. All crystal structures were visualized using the VESTA code Momma:vesta. b The distortion amplitude of different distortion modes and calculated enthalpies (H = E + PV) of different structures, as a function of pressure. c The enthalpy of the P4/mmm phase was taken as the reference energy. c The $A^{5+}$ distortion amplitudes vs. pressure for different $U_{\rm eff}$.
• Figure 4: Electronic structure of 1212-LNO in the P4/mmm phase.a Alignment of $e_g$ levels. Light blue (pink) horizontal lines represent $d_{3z^2-r^2}$ ($d_{x^2-y^2}$) states. $d_{3z^2-r^2}$ orbitals from the BL sublattice show bonding-antibonding splitting, while $d_{3z^2-r^2}$ orbital coming from the SL sublattice does not show such splitting. b The projected DFT band structure of the P4/mmm phase of 1212-LNO at 20 GPa. The coordinates of the high-symmetry points in the Brillouin zone are $\Gamma$ = (0, 0, 0), X = (0, 0.5, 0), M = (0.5, 0.5, 0), Z = (0, 0, 0.5), R = (0, 0.5, 0.5) and A = (0.5, 0.5, 0.5). c Tight-binding band structure and d Fermi surface for the P4/mmm phase of 1212-LNO at 20 GPa. The input file of the hopping matrices and crystal-field splittings can be found in a separate attachment in the Supplemental Materials. The tight-binding results at other pressures can be found in Supplementary Note III.
• Figure 5: RPA superconducting gap structure $g({\bf k})$ of 1212-LNO at 20 GPa.a Leading $d_{x^2-y^2}$-wave state with $\lambda=0.1878$; b Subleading $g$-wave state with $\lambda=0.0882$; c Subleading $d_{xy}$-wave state with $\lambda=0.0869$; d Subleading $s^\pm$-wave state with $\lambda=0.0829$. The sign of $g_\alpha({\bf k})$ is indicated by the color (orange = positive, blue = negative), and its amplitude by the point sizes. Here we used Coulomb parameters $U=0.55$ eV, $U'=U/2$, and $J=J'=U/4$, and the calculation was performed for a temperature of $T=0.02$ eV.