Preempted phonon-mediated superconductivity in the infinite-layer nickelates

Nickelate superconductors are outstanding materials with intriguing analogies with the cuprates. These analogies suggest that their superconducting mechanism may be unconventional, although this fundamental question is currently under debate. Here, we scrutinize the role played by electronic correlations in enhancing the electron-phonon coupling in the infinite-layer nickelates and the extent to which this may promote superconductivity. Specifically, we use ab initio many-body perturbation theory to perform state-of-the-art $GW$ and Eliashberg-theory calculations. We find that the electron-phonon coupling is effectively enhanced compared to pure density-functional-theory calculations. This enhancement may lead to low-$T_c$ superconductivity in the parent compounds already. However, it remains marginal in the sense that it cannot explain the record $T_c\mathrm{s}$ obtained with doping. This circumstance implies that conventional superconductivity is preempted by another pairing mechanism in the infinite-layer nickelates.

Figure 1

(Left panel) Crystal structure of the infinite-layer nickelates $R{\mathrm{NiO}}_2$ with nickel atoms in blue, oxygens in red, and rare earth in orange. (Middle and right panels) Top view of the characteristic Fermi surface of these systems with the main $\text{Ni-}3d_{x^2-y^2}$ sheet in blue and the additional rare-earth derived sheets (self-doping) in orange.

Figure 2

Band structure of ${\mathrm{Nd}}_{0.8}{\mathrm{Sr}}_{0.2}{\mathrm{NiO}}_2$ near the Fermi level calculated within the $GW$ approximation for the self-energy. The different panels correspond to different treatments of the screening via the contour deformation technique (red), the Godby-Needs plasmon-pole model (blue) and the Hybertsen-Louie one (green), with the DFT result in gray. Compared with the numerically exact $GW$-CD method, the plasmon-pole models tend to overestimate the self-doping effect ( i.e., the dipping of the bands down the Fermi level at $\mathrm{\Gamma }$ and A).

Figure 3

(a) Total and site-resolved phonon density of states, (b) Eliashberg spectral function ${\alpha }^{2}F\left(\omega \right)$ (solid lines) and corresponding cumulative coupling constant $\lambda \left(\omega \right)={\int }_0^{\omega }d{\omega }^{\prime }{\alpha }^{2}F\left({\omega }^{\prime }\right)/{\omega }^{\prime }$ (dashed lines) and (c) distribution of electron-phonon coupling strength ${\lambda }_{\mathbf{k}{\mathbf{k}}^{\prime }}$ calculated for ${\mathrm{Nd}}_{0.8}{\mathrm{Sr}}_{0.2}{\mathrm{NiO}}_2$. The different curves in (b) and (c) correspond to different approximations for the electronic structure [DFT vs $GW$ using the numerically exact contour-deformation (CD) technique as well as GN and HL plasmon-pole models].

Figure 4

(a) Computed $GW$ band structure and DOS of ${\mathrm{Nd}}_{0.8}{\mathrm{Sr}}_{0.2}{\mathrm{NiO}}_2$ as a function of pressure. The DOS at the Fermi level is $N_F=1.44$, 1.40, 1.37, 1.33, and 1.24 states/eV unit cell for 0, 6, 12, 24, and 36 GPa, respectively. (b) Eliashberg function ${\alpha }^{2}F\left(\omega \right)$ and electron-phonon coupling constant $\lambda ,$ and (c) distribution of electron-phonon coupling strength ${\lambda }_{\mathbf{k}{\mathbf{k}}^{\prime }}$ associated with the electronic structures in (a).