The ruthenate family of layered perovskites has been a topic of intense interest with much work dedicated to understanding the superconducting state of the single layer, Sr$_2$RuO$_4$. Another longstanding puzzle is the lack of superconductivity in its sister compound, Sr$_3$Ru$_2$O$_7$, which constrains the possible superconducting mechanisms of Sr$_2$RuO$_4$. Here we address a microscopic mechanism that unifies superconducting and spin-density wave order in this family of materials. Beginning from a model of Sr$_2$RuO$_4$ featuring intraband pseudospin-singlet superconductivity originating from interorbital spin-triplet pairing via Hund's and spin-orbit couplings, the addition of bilayer coupling and staggered rotations of the oxygen octahedra are investigated. We find that the bilayer coupling alone enhances superconductivity, while staggered rotations destroy interorbital superconductivity, leaving a paramagnetic metal. The magnetic field then shifts van Hove singularities near the Fermi level, allowing intraorbital SDW order to form in the bilayer. Our theory predicts that bilayer Sr$_3$Ru$_2$O$_7$ without staggered rotations exhibits interorbital superconductivity with a possibly higher transition temperature. 

Evolution of interorbital superconductor to intraorbital spin-density wave in layered ruthenates

Metamagnetic materials enable control of the ground state through applied magnetic fields. Understanding the microscopic origin of metamagnetism promises tuneability for new technological functionalities. Here, the authors use quasiparticle interference, magnetization measurements, and dilatometry in vector magnetic fields to establish the interplay between magnetism, spin-orbit coupling, microscopic electronic structure, and crystal structure of the trilayer ruthenate Sr${}_{4}$Ru${}_{3}$O${}_{10}$. These results reveal a surprising anisotropy in the properties of the material, highlighting the role of spin-orbit coupling. 

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Interplay of ferromagnetism and spin-orbit coupling in 
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Recently, the search of superconducting materials with topological states has attracted extensive interest due to their exotic properties. By using first-principles calculations, we predict that RuC monolayer is a two-dimensional topological insulator (TI) and shows a TI–superconductor transition under electron doping, leading to a superconducting transition temperature T c of 1.4 K. Further analysis reveals that the emergence of superconductivity in RuC depends critically on the existence of flatband optical phonons as well as the appearance of multiple electron-pockets and phonon mode softening induced by doping. Moreover, we find that Li-intercalated RuC (LiRuC) is a thermal dynamically stable, superconducting material with a high T c of 9.8 K, benefitting from the strong electron–phonon coupling. Many other superconductors with flat phonon bands are also predicted via elemental substitution in LiRuC. Our results will broaden the research interest in exploring more superconductors and modulating their physical properties through flat phonon bands. 

Soft-mode-phonon-mediated insulator–superconductor transition in doped two-dimensional topological insulator RuC

We report electronic band structure calculations for Sr$_{4}$Ru$_{3}$O$_{10}$ that displays both ferromagnetic and metamagnetic behavior. The density functional calculations find the ground state to be ferromagnetic in agreement with the experiment and we find that the inclusion of Coulomb Hubbard interaction U applied to the Ru 4d states has dramatic effects on the Fermi surface, which reveal the role of Coulomb interactions and correlated many-body physics. The minority spin bands are mainly empty with Fermi surfaces in the outer areas of the Brillouin zone away from the $\Gamma$ point with bands that disperse steeply upward. The majority spin bands are full or nearly fully occupied and form narrow bands near the Fermi energy around the $\Gamma$ point, which could be the electronic origin of the metamagnetism. The results are in qualitative agreement with recent angle resolved photoemission spectroscopy (ARPES) experiments and show the need for a combined theoretical study and experimental ARPES investigation with better energy resolution to reveal the nature of the narrow bands close to the Fermi-level, which is critical for understanding the exotic magnetic properties observed in this material.

Omololu Akin-Ojo

Papers

Electronic Structure and Magnetism of the Triple-layered Ruthenate Sr$_{4}$Ru$_{3}$O$_{10}$