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The discovery of superconductivity at 80 K under high pressure in La$_3$Ni$_2$O$_7$ presents the groundbreaking confirmation that high-$T_c$ superconductivity is a property of strongly correlated materials beyond cuprates. We use density…

Motivated by the recent discovery of superconductivity in square-planar nickelates as well as by longstanding puzzling experiments in heavy-fermion superconductors, we study Cooper pairing between correlated $d$-electrons coupled to a band…

The recent discovery of bulk superconductivity in trilayer nickelate La$_4$Ni$_3$O$_{10}$ with the critical temperature $T_c$ near $30$K under high pressure is attracting a new wave of research interest, after the breakthrough of bilayer…

We study the phase diagram of the Hubbard model in the weak-coupling limit for coexisting spin-density-wave order and spin-fluctuation-mediated superconductivity. Both longitudinal and transverse spin fluctuations contribute significantly…

Superconductivity in alkali-intercalated iron selenide, with T_c's of 30K and above, may have a different origin than that of the other Fe-based superconductors, since it appears that the Fermi surface does not have any holelike sheets…

Contrary to the usual assumption, the electron Bloch states in crystals with spin-orbit coupling do not always transform under symmetry operations in the same way as the pure spin-1/2 states. This has profound consequences for the symmetry…

After decades of fundamental research, unconventional superconductivity has recently been demonstrated in rare-earth infinite-layer nickelates. The current view depicts these systems as a new category of superconducting materials, as they…

Starting from an effective two-dimensional two-band model for infinite layered nickelates, consisting of bands obtained from $d$ and $s$--like orbitals, we investigate to which extend it can be mapped onto a single-band Hubbard model. We…

Monolayer superconducting transition metal dichalcogenide NbSe$_2$ is a candidate for a nodal topological superconductor by magnetic field. Because of the so-called Ising spin-orbit coupling that strongly pins the electron spins to the…

We propose a scenario for superconductivity at strong electron-electron attractive interaction, in the case when the increase of the interaction strength promotes the nucleation of the local Cooper pairs and forms a state with a spatially…

Ruddlesden-Popper (RP) nickelates have emerged as a crucial platform for exploring the mechanisms of high-temperature superconductivity. However, the Fermi surface topology required for superconductivity remains elusive. Here, beyond the…

Signatures of superconductivity under pressure have recently been reported in the bilayer La$_3$Ni$_2$O$_7$ and trilayer La$_4$Ni$_3$O$_{10}$ Ruddlesden-Popper (RP) nickelates with general chemical formula La$_{n+1}$Ni$_n$O$_{3n+1}$ ($n=$…

The recently discovered superconductivity in Nd$_{1-x}$Sr$_x$NiO$_2$ provides a new opportunity for studying strongly correlated unconventional superconductivity. The single-hole Ni$^+$ ($3d^9$) configuration in the parent compound…

A striking series of experiments have observed superconductivity in Bernal-stacked bilayer graphene (BBG) when the energy bands are flattened by applying an electrical displacement field. Intriguingly, superconductivity manifests only at…

Recently, the bulk nickelate La$_3$Ni$_2$O$_7$ is reported to show signature of high-temperature superconductivity under high pressure above $14$GPa [H. Sun et al., Nature 621, 493 (2023)]. We analyze the pairing mechanism and pairing…

We explore the superconducting properties of the bilayer Hubbard model, which exhibits a high transition temperature ($T_{\rm c}$) for an $s_{\pm}$ pairing, using a cluster extension of the dynamical mean-field theory. Unlike the…

We show how the pairing symmetry of superconducting states in twisted bilayer graphene can be experimentally identified by theoretically studying effects of externally applied in-plane magnetic field and strain. In the low field regime,…

The recently discovered superconducting infinite-layer nickelates offer a novel platform to explore an exotic pairing mechanism in multi-band systems towards high-temperature superconductivity and associated rich quantum phases, contrasting…

The dynamics of Higgs mode in superconductors, manifested as coherent oscillations of the superconducting order parameter amplitude, provides vital insights into the nature of the superconducting gap structure and symmetry. Here we utilize…

We study the electronic structure and doping-dependent instabilities of strained La$_3$Ni$_2$O$_7$ thin films using first-principles and functional renormalization group methods. We demonstrate that ordering tendencies are governed by Fermi…