Unconventional superconductivity without doping in infinite-layer nickelates under pressure

The discovery of high-temperature superconductivity in LaBaCuO₄ sparked extensive research into unconventional superconductors and their pairing mechanisms. The subsequent discovery of superconductivity in infinite-layer nickelates (A_1-xB_xNiO₂, where A represents rare earths and B alkaline earths) provided a new avenue for understanding this phenomenon. Nickelates exhibit striking similarities to cuprates, suggesting a common underlying mechanism, yet also crucial differences. While superconductivity in nickelates displays a dome-like shape typical of unconventional superconductors and is relatively independent of the rare earth and dopant elements, the theoretical understanding has remained varied due to the complexity of strong electronic correlations. Previous theoretical work using a one-orbital Hubbard model for the Ni d_x2-y2 band, coupled with electron pockets acting as electron reservoirs, accurately predicted the superconducting dome in Sr-doped NdNiO₂. This success motivated the current research to investigate the effect of pressure on these materials, particularly following experimental findings demonstrating a significant increase in T_c under pressure in Sr_xPr_1-xNiO₂ films. The study aims to quantitatively model the pressure-dependent superconducting phase diagram and explore the possibility of achieving even higher T_c values.

Several theoretical models have been proposed to explain superconductivity in nickelates, owing to the challenge of incorporating strong electronic correlations. These models have focused on both similarities and differences between nickelates and cuprates. The similarities include the crystal and electronic structure, while the differences encompass aspects such as the energy separation of Ni³⁺ 3d bands from oxygen ones, weaker hybridization, and the role of rare-earth A-derived bands that form electron pockets, self-doping the Ni d_x2-y2 band and preventing the parent compound from being an antiferromagnetic insulator. Previous work by Kitatani et al. successfully predicted the superconducting dome in Sr-doped NdNiO₂ using a minimal one-orbital Hubbard model for the Ni d_x2-y2 band plus decoupled electron pockets. The excellent agreement between their predictions and experimental results, including the quantitative T_c, doping range, and dome skewness, solidified the relevance of this minimal model. Recent experimental work by Wang et al. demonstrated a significant increase in T_c in Sr_xPr_1-xNiO₂ under pressure, providing the impetus for the present study.

The researchers utilized a state-of-the-art computational scheme combining density functional theory (DFT), dynamical mean-field theory (DMFT), and the dynamical vertex approximation (DIA). To simulate the effect of isotropic pressure applied in a diamond anvil cell to the nickelate films grown on a SrTiO₃ (STO) substrate, they first calculated the STO equation of state in DFT to obtain lattice parameters under pressure. Then, they fixed the in-plane lattice parameters to those of the pressurized STO and determined the out-of-plane lattice parameter (c) that minimized the enthalpy at each pressure. This approach accurately reflects the experimental pressure conditions. Using these crystal structures, DFT electronic structure calculations were performed at various pressures (0, 12, 50, 100, and 150 GPa). Wannierization was then performed to generate a 10-orbital and a 1-orbital model. The 10-orbital model included all Pr-d and Ni-d orbitals, while the 1-orbital model focused solely on the Ni d_x2-y2 orbital. The DFT Wannier Hamiltonians were supplemented with local intra-orbital Coulomb interactions (U and Hund's exchange J) determined by the constrained random phase approximation (CRPA). DMFT calculations were performed for both models, obtaining the spectral function. A one-band minimal model for superconductivity was justified based on the low-energy physics of the 10-band model, using the effective hole doping of the Ni d_x2-y2 band calculated from the 10-band DFT+DMFT results. Finally, the superconducting T_c was calculated using DIA, considering different paths in parameter space: as a function of doping at different pressures, and as a function of pressure at fixed doping levels (including the undoped case).

The study's main findings are summarized as follows: (1) A strong increase in hopping (t) by almost a factor of two was observed when pressure increased from 0 to 150 GPa, while the interaction (U) remained relatively unchanged, similar to cuprates. (2) Pressure led to deeper electron pockets, enhancing the hole doping (δ) of the Ni d_x2-y2 band. (3) At 50 GPa, the maximum T_c was doubled compared to ambient pressure, with superconductivity observed across a much wider doping range, extending to the undoped case. (4) For the experimentally investigated Sr-doping (x=0.18), the calculated T_c increase (0.81 K/GPa) closely matched experimental results (0.96 K/GPa) up to 12 GPa. The model slightly overestimated the T_c at 0 GPa (30 K vs experimental 18 K), but remained in good agreement. (5) Beyond 12 GPa, T_c continued to rise to 49 K at 50 GPa before decreasing. (6) Most notably, the undoped parent compound (PrNiO₂) showed superconductivity above 50 GPa, peaking at nearly 100 K around 100 GPa. This high T_c arises solely from the increased self-doping induced by pressure. (7) Analysis of the results revealed that the pressure-induced increase in hopping (t) and the enhanced self-doping from the growing electron pockets are the key factors driving the enhanced superconductivity. (8) The decrease in T_c above 50 GPa, observed with Sr-doping, is attributed to the shift from optimal to overdoped regime with increased pressure. In contrast, for the undoped case, the system moves from an underdoped to an optimal doping level with pressure. (9) The data shows that the maximum Tc is predicted to be found in the undoped PrNiO2 between 50 and 100 GPa. This result places nickelates almost on par with cuprates in terms of high-Tc superconductivity. (10) An alternative pathway to achieve similar in-plane lattice compression was suggested, using substrates with smaller lattice parameters (like LaAlO₃, YAlO₃, and LuAlO₃). This approach might yield higher T_c but only with at least 10% doping.

The findings strongly suggest that the current experimental investigations of infinite-layer nickelates are far from reaching their maximum T_c. The surprising prediction of a nearly 100 K T_c in undoped PrNiO₂ under pressure (50-100 GPa) places nickelates among the leading high-T_c superconductors. The pressure-induced changes in the phase diagram, including increased T_c and a wider superconducting dome shifted to lower doping at high pressure, are explained by the interplay between pressure-enhanced hopping and self-doping from the expanding electron pockets. The decrease in T_c at very high pressures in the Sr-doped system is consistent with overdoping, whereas in the undoped system it is associated with pressure decreasing U/t below the optimal value. The potential to achieve similar effects using alternative substrates with smaller lattice parameters, such as LaAlO₃, YAlO₃, and LuAlO₃, opens up new experimental avenues for further enhancing T_c, although likely requiring a minimum doping level.

This study provides compelling evidence that high-pressure synthesis significantly enhances the superconducting properties of infinite-layer nickelates, with the potential to achieve T_c values comparable to cuprates. The remarkable prediction of a high T_c in the undoped parent compound highlights the significant role of pressure-induced self-doping. Future research should focus on experimental validation of these predictions at higher pressures and exploration of alternative substrates to further optimize the superconducting properties of these materials.

The study relies on computational modeling and makes predictions that need experimental verification. The accuracy of the model depends on the accuracy of the approximations used in DFT, DMFT, and DIA. The assumptions of the minimal model, particularly the decoupling of electron pockets, need further investigation. While the pressure effects are simulated realistically, subtle variations in the experimental conditions may affect the results. The effect of the substrate and interface have not been directly taken into account beyond the impact on lattice parameters.