Theoretical and computational overview of high T_c superconductivity in nickelates

The discovery of superconductivity in the infinite layer nickelates started a novel field within unconventional superconductivity, providing also the opportunity to understand the differences and similarities with the cuprates [1]. In addition, the recent observation of pressure-induced superconductivity at 80K in the bilayer La₃Ni₂O₇ (LNO), as well as in the trilayer La₄Ni₃O₁₀, different from the previously studied infinite layer nickelates, has unveiled a vast and exciting window into high-Tc superconductivity where now the Ni orbital degrees of freedom play a key role.

We investigated theoretically the whole family of bilayer 327-type nickelates R₃Ni₂O₇ (R = rare-earth elements from La to Lu) [2,3,5,6,9], as well as the non-superconducting bilayer La₃Ni₂O₆ [4], and the trilayer La₄Ni₃O₁₀ [7], all under pressure, and we also studied the hybrid stacking nickelate superlattice La₇Ni₅O₁₇ [8]. Initial studies using density functional theory (DFT) allowed to identify a structural phase transition that occurs under pressure [2] and the relevance of two active orbitals, d_3z2−r2 and d_x2−y2, near the Fermi energy, instead of just one active orbital as in the cuprates. This allowed us to construct a two-orbital model Hamiltonian with Hubbard and Hund interactions, and crystal field, whose parameters and geometry were adapted to each of the investigated materials [2-9] and studied using primarily the random phase approximation (RPA) to incorporate electronic correlations. Some results were also obtained with the density matrix renormalization group (DMRG)[9]. Our primary RPA result is that the s±-wave pairing tendency, similar to that of Fe-based superconductors, dominates the multilayer structures, due to the nesting between the M = (π,π) and the X = (π , 0) and Y = (0, π) points in the Brillouin zone [4]. The nesting is associated to magnetic tendencies that were observed in our calculations and indeed the lack of nesting and pockets around M = (π,π) in La₃Ni₂O₆ may explain the absence of superconductivity in this material [3]. Results on the magnetic effects of doping will be discussed as well [9].