Optimizing Superconductivity: From Cuprates via Nickelates to Palladates

Origin and fate of the pseudogap in the doped Hubbard model

The relationship between the pseudogap and underlying ground-state phases has not yet been rigorously established. We investigated the doped two-dimensional Hubbard model at finite temperature using controlled diagrammatic Monte Carlo calculations, allowing for the computation of spectral properties in the infinite-size limit and with arbitrary momentum resolution. We found three distinct regimes as a function of doping and interaction strength: a weakly correlated metal, a correlated metal with strong interaction effects, and a pseudogap regime at low doping. We show that the pseudogap forms both at weak coupling, when the magnetic correlation length is large, and at strong coupling, when it is shorter. As the temperature goes to zero, the pseudogap regime extrapolates precisely to the ordered stripe phase found by ground-state methods.

Evidence for d-wave superconductivity of infinite-layer nickelates from low-energy electrodynamics

The discovery of superconductivity in infinite-layer nickelates established another category of unconventional superconductors that shares structural and electronic similarities with cuprates. However, key issues of the superconducting pairing symmetry, gap amplitude and superconducting fluctuations are yet to be addressed. Here we utilize static and ultrafast terahertz spectroscopy to address these. We demonstrate that the equilibrium terahertz conductivity and non-equilibrium terahertz responses of an optimally Sr-doped nickelate film (superconducting transition temperature of Tc = 17 K) are in line with the electrodynamics of d-wave superconductivity in the dirty limit. The gap-to-Tc ratio (2Δ/kBTc) is found to be 3.4, indicating that the superconductivity falls in the weak coupling regime. In addition, we observed substantial superconducting fluctuations near Tc that do not extend into the deep normal state as the optimally hole-doped cuprates do. Our results support a d-wave system that closely resembles the electron-doped cuprates.

Unconventional superconductivity without doping in infinite-layer nickelates under pressure

High-temperature unconventional superconductivity quite generically emerges from doping a strongly correlated parent compound, often (close to) an antiferromagnetic insulator. The recently developed dynamical vertex approximation is a state-of-the-art technique that has quantitatively predicted the superconducting dome of nickelates. Here, we apply it to study the effect of pressure in the infinite-layer nickelate SrxPr1-xNiO2. We reproduce the increase of the critical temperature (Tc) under pressure found in experiment up to 12 GPa. According to our results, Tc can be further increased with higher pressures. Even without Sr-doping the parent compound, PrNiO2, will become a high-temperature superconductor thanks to a strongly enhanced self-doping of the Nid x 2 - y 2 orbital under pressure. With a maximal Tc of 100 K around 100 GPa, nickelate superconductors can reach that of the best cuprates.

Transfer learning from Hermitian to non-Hermitian quantum many-body physics

Identifying phase boundaries of interacting systems is one of the key steps to understanding quantum many-body models. The development of various numerical and analytical methods has allowed exploring the phase diagrams of many Hermitian interacting systems. However, numerical challenges and scarcity of analytical solutions hinder obtaining phase boundaries in non-Hermitian many-body models. Recent machine learning methods have emerged as a potential strategy to learn phase boundaries from various observables without having access to the full many-body wavefunction. Here, we show that a machine learning methodology trained solely on Hermitian correlation functions allows identifying phase boundaries of non-Hermitian interacting models. These results demonstrate that Hermitian machine learning algorithms can be redeployed to non-Hermitian models without requiring further training to reveal non-Hermitian phase diagrams. Our findings establish transfer learning as a versatile strategy to leverage Hermitian physics to machine learning non-Hermitian phenomena.