At a temperature of roughly 1 K, Sr2RuO4 undergoes a transition from a normal Fermi liquid to a superconducting phase. Even while the former is relatively simple and well understood, the superconducting state has not even been understood after 25 years of study. More recently, it has been found that critical temperatures can be enhanced by the application of uniaxial strain, up to a critical strain, after which it falls off. In this work, we take an “instability” approach and seek divergences in susceptibilities. This provides an unbiased way to distinguish tendencies to competing ground states. We show that in the unstrained compound, the singlet and triplet instabilities of the normal Fermi liquid phase are closely spaced. Under uniaxial strain, electrons residing on all orbitals contributing to the Fermiology become more coherent, while the electrons of the Ru-dxy character become heavier, and the electrons of the Ru-dxz,yz characters become lighter. In the process, Im χ(q,ω) increases rapidly around q = (0.3,0.3,0)2π/a and q = (0.5,0.25,0)2π/a, while it gets suppressed at all other commensurate vectors, in particular at q = 0, which is essential for spin-triplet superconductivity. We observe that the magnetic anisotropy under strain drops smoothly, which is concomitant with the increment in singlet instability. Thus, the triplet superconducting instability remains the lagging instability of the system, and the singlet instability enhances under strain, leading to a large energy-scale separation between these competing instabilities. However, since this happens even without spin-orbit coupling, we believe it is primarily the enhancement in the spin fluctuation glue around quasi-anti-ferromagnetic vectors that drives the Cooper pairing instead of the magnetic anisotropy. At large strain, an instability to a spin density wave overtakes the superconducting one. The analysis relies on a high-fidelity, ab initio description of the one-particle properties and two-particle susceptibilities, based on the quasiparticle self-consistent GW approximation augmented by dynamical mean field theory. This approach is described and its high fidelity confirmed by comparing to observed one- and two-particle properties.

Lanthanide hydrogen-rich materials have long been considered as one of the candidates with high-temperature superconducting properties in condensed matter physics, and have attracted great interest. Attempts to investigate the effects of different compositions of lanthanide hydrogen-rich materials are ongoing, with predictions and experimental studies in recent years having shown that substances such as LaH10, CeH9, and LaH16 exhibit extremely high superconducting temperatures between 150-250 GPa. In particular, researchers have noted that in those materials an increase in the f character at the Fermi level leads to an increase in the superconducting temperature. Here, we further elaborate on the effect of the ratios of lanthanide to hydrogen in these substances with the aim to bring more clarity to the study of superhydrides in these extreme cases by comparing a variety of lanthanide hydrogen-rich materials with different ratios using the DMFT method, and provide ideas for later structural predictions and material property studies.

Lanthanide hydrogen-rich materials have long been considered as one of the candidates with high-temperature superconducting properties in condensed matter physics, and have been a popular topic of research. Attempts to investigate the effects of different compositions of lanthanide hydrogen-rich materials are ongoing, with predictions and experimental studies in recent years showing that substances such as LaH10, CeH9, and LaH16 exhibit extremely high superconducting temperatures between 150–250 GPa. In particular, researchers have noted that, in those materials, a rise in the f orbit character at the Fermi level combined with the presence of hydrogen vibration modes at the same low energy scale will lead to an increase in the superconducting transition temperature. Here, we further elaborate on the effect of the ratios of lanthanide to hydrogen in these substances with the aim of bringing more clarity to the study of superhydrides in these extreme cases by comparing a variety of lanthanide hydrogen-rich materials with different ratios using the dynamical mean-field theory (DMFT) method, and provide ideas for later structural predictions and material property studies.