Advances in Superconducting Infinite-Layer and Related Nickelates

After the reward of more than 2 decades of pursuit on the high-T_c cuprate analog with the hope to obtain a better understanding of the mechanism of high-T_c superconductivity, the discovery of superconductivity in the infinite-layer nickelate brings more mystery to the picture than expected. Tops in the list of questions are perhaps 1) absence of superconductivity in the bulk nickelate and limited thickness of the infinite-layer phase in thin film, 2) absence of superconductivity in the La-nickelate despite it being the earliest studied rare-earth nickelate, and the role of 4 $f$ orbital in the recipe of superconductivity, 3) absence of Meissner effect and suspect of the origin of superconductivity from the interface, 4) whether nickelate hosts similar pairing symmetry to the single-band high-T_c cuprates or multiband iron-based superconductor. In this perspective article, we will discuss the following aspects: 1) stabilization of the infinite-layer phase on the SrTiO₃(001) substrate and the thickness dependency of observables; 2) rare-earth dependence of the superconducting dome and phase diagram of the (La/Pr/Nd)- infinite-layer nickelate thin film; 3) experimental aspects of the measurement of Meissner effect; 4) theoretical framework and experimental study of the pairing symmetry of infinite-layer nickelate superconductor.

This article summarizes recent work on the many-body (beyond density functional theory) electronic structure of layered rare-earth nickelates, both in the context of the materials themselves and in comparison to the high-temperature superconducting (high-T_c) layered copper-oxide compounds. It aims to outline the current state of our understanding of layered nickelates and to show how the analysis of these fascinating materials can shed light on fundamental questions in modern electronic structure theory. A prime focus is determining how the interacting physics defined over a wide energy range can be estimated and “downfolded” into a low energy theory that would describe the relevant degrees of freedom on the ∼$0.5$  eV scale and that could be solved to determine superconducting and spin and charge density wave phase boundaries, temperature dependent resistivities, and dynamical susceptibilities.

We review the electronic structure of nickelate superconductors with and without effects of electronic correlations. As a minimal model, we identify the one-band Hubbard model for the Ni 3$d_{x^2-y^2}$ orbital plus a pocket around the A-momentum. The latter, however, merely acts as a decoupled electron reservoir. This reservoir makes a careful translation from nominal Sr-doping to the doping of the one-band Hubbard model mandatory. Our dynamical mean-field theory calculations, in part already supported by the experiment, indicate that the Γ pocket, Nd 4f orbitals, oxygen 2p, and the other Ni 3d orbitals are not relevant in the superconducting doping regime. The physics is completely different if topotactic hydrogen is present or the oxygen reduction is incomplete. Then, a two-band physics hosted by the Ni 3$d_{x^2-y^2}$ and 3$d_{3z^2-r^2}$orbitals emerges. Based on our minimal modeling, we calculated the superconducting T_c vs. Sr-doping x phase diagram prior to the experiment using the dynamical vertex approximation. For such a notoriously difficult to determine quantity as T_c, the agreement with the experiment is astonishingly good. The prediction that T_c is enhanced with pressure or compressive strain has been confirmed experimentally as well. This supports that the one-band Hubbard model plus an electron reservoir is the appropriate minimal model.