Interplay of orbital-selective Mott criticality and flat-band physics in La$_3$Ni$_2$O$_6$

TL;DR

This work addresses $La_3Ni_2O_6$, a reduced bilayer nickelate with nominal Ni$^{1.5+}$, and assesses its potential to bridge the $3d^9$- and $3d^8$-like superconducting nickelate families using first-principles many-body theory. It reveals a novel correlated (quasi-)insulating state in which Ni-$d_{x^2-y^2}$ electrons are orbital-selectively Mott localized while a Ni-$d_{z^2}$ flat band becomes gapped through scattering with the localized moments, describable as a ferromagnetic Kondo-lattice scenario. The charge gap is found to be about $50$ meV and remains robust under hole doping up to about $x<0.15$, after which the flat-band state is released and a low-energy quasiparticle resonance with predominant Ni-$d_{z^2}$ character appears. Spin/charge fluctuations computed in the RPA framework yield an $s_cpm$-wave superconducting instability with a strong interlayer component, suggesting the possibility of ambient-pressure unconventional superconductivity in $La_3Ni_2O_6$ and providing a concrete link between RP and infinite-layer nickelate superconductors.

Abstract

Superconductivity in nickelates apparently takes place in two different Ni oxidation regimes, namely either for infinite-layer-type compounds close to Ni$^{+}$, or for Ruddlesden-Popper materials close to Ni$^{2+}$. The reduced La$_3$Ni$_2$O$_6$ bilayer with a nominal Ni$^{1.5+}$ oxidation state may therefore serve as a normal-state mediator between the two known families of $3d^8$-like and $3d^9$-like superconducting nickelates. Using first-principles many-body theory, we explain its experimental 50\,meV charge gap as originating from a new type of correlated (quasi-)insulator. Flat-band electrons of Ni-$d_{z^2}$ character become localized from scattering with orbital-selective Mott-localized Ni-$d_{x^2-y^2}$ electrons, by trading in residual hopping energy for a gain in local exchange energy in a ferromagnetic Kondo-lattice scenario. Most importantly, the flat-band electrons offer another route to unconventional superconductivity in nickelates at ambient pressure.

Figures (5)

• Figure 1: Reduced bilayer compound La$_3$Ni$_2$O$_6$. (a) Tetragonal $I4/mmm$ crystal structure with La(green), Ni(blue) and O(red) atoms. (b) DFT dispersions in fatspec representation highlighting the Ni$(3d)$ orbital characters.
• Figure 2: Spectral properties of La$_3$Ni$_2$O$_6$ from DFT+sicDMFT at $T=50$ K. (a) Upper panel: total and projected k-integrated spectral function (inset: low-energy blow up). Lower panel: Ni$(3d)$ local spectral function. Right inset: low-energy blow up. (b) k-resolved spectral function $A({\bf k},\omega)$ along high-symmetry lines. (c) Fatspec representation of $A({\bf k},\omega)$ for the different Ni$(3d)$ contributions (DFT bands: grey lines).
• Figure 3: Effect of temperature on the Ni-$e_g$ states of La$_3$Ni$_2$O$_6$ from DFT+sicDMFT. (a) Temperature dependence of low-energy spectral function (left), and respective imaginary part of the Matsubara self-energy $\Sigma(i\omega_n)$ (right). (b) Fatspec representation of the k-resolved spectral function $A({\bf k},\omega)$ for $T=150$ K.
• Figure 4: Spectral properties of hypothetical (La$_{1-x}$Sr$_x$)$_3$Ni$_2$O$_6$ at $T=50$ K based on DFT+sicDMFT using VCA for the doped La sites. (a) Total spectral function (inset: low-energy blow up). (b) Bloch-resolved spectral function $A_\nu(\omega)$ for $\nu=\nu_{\rm f}$ (variants of red) and for $\nu=\nu_{\rm f}\pm 1$ (grey), with $\nu_{\rm f}$ denoting the Bloch state, largest susceptible to hole doping. (c) Ni-$e_g$-resolved local spectral function (inset: low-energy blow up for Ni-$d_{z^2}$). (d,e) Fatspec representation of the k-resolved spectral function $A({\bf k},\omega)$, and the Fermi surface in the $k_z=0$ plane for $x=0.225$. Color coding of (d,e) as in Fig. \ref{['fig2']}c.
• Figure 5: Spin susceptibility and superconducting gap function for the lowest positive Matsubara frequency of the Ni-$d_{z^2}$-orbital component in the first Brillouin zone. Note that the even susceptibility in (a) is an order of magnitude smaller than the odd susceptibility in (b). The real part of the intra- and interlayer superconducting gap functions are shown in (c) and (d), respectively. The susceptibility is given in units of states/eV, and the superconducting gaps are in units of meV.