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An important challenge in condensed matter physics is understanding iron-based superconductors. Among these systems, the iron selenides hold the record for highest superconducting transition temperature and pose especially striking puzzles…

A major puzzle about the nature of the iron-based superconductivity appears in the case of the alkaline iron selenides. Compared to the iron pnictides, these systems have only electron Fermi pockets (i.e. no hole Fermi pockets) but…

Heavy-fermion superconductors are prime candidates for novel electron-pairing states due to the spin-orbital coupled degrees of freedom and electron correlations. Superconductivity in CeCu$_2$Si$_2$ discovered in 1979, which is a prototype…

I review theoretical ideas and implications of experiments for the gap structure and symmetry of the Fe-based superconductors. Unlike any other class of unconventional superconductors, one has in these systems the possibility to tune the…

Fermionic superfluidity with a nontrivial Cooper-pairing, beyond the conventional Bardeen-Cooper-Schrieffer state, is a captivating field of study in quantum many-body systems. In particular, the search for superconducting states with…

Using the constraints imposed by the crystalline symmetry of FeSe and the experimentally observed phenomenology, we analyze the possible pairing symmetry of the superconducting order parameter focusing on intercalated and monolayer FeSe…

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…

We demonstrate that strong inter-orbital interaction is very efficient to achieve superconductivity due to magnetic fluctuations in the iron pnictides. Fermi surface states that are coupled by the antiferromagnetic wave vector are often of…

In the two-dimensional Kondo-Heisenberg lattice model away from half-filled, the local antiferromagnetic exchange coupling can provide the pairing mechanism of quasiparticles via the Kondo screening effect, leading to the heavy fermion…

Noncentrosymmetric superconductors with various types of pairing interactions are systematically examined with particular focus on phenomena that originate from the differences between Fermi surfaces split by a strong spin-orbit coupling.…

Motivated by the fully gapped superconductivity in iron-based superconductors with uncompensated electron pockets, we propose a spin singlet, but orbital triplet analogue of the superfluid phase of He-3B. We show that orbital triplets with…

The heavy-fermion system $\mathrm{UTe_2}$ is a candidate for spin-triplet superconductivity, which is of considerable interest to quantum engineering. Among the outstanding issues is the nature of the pairing state. A recent surprising…

We study the superconducting state in newly discovered high-Tc superconductor K$_x$Fe$_2$Se$_2$ based on the ten-orbital Hubbard-Holstein model without hole-pockets. When the Coulomb interaction is large, spin-fluctuation mediated d-wave…

We investigate superconductivity that may exist in the doped BaCoSO, a multi-orbital Mott insulator with a strong antiferromagnetic ground state. The superconductivity is studied in both t-J type and Hubbard type multi-orbital models by…

Multiband superconductivity with dominant two-gap features are recently proposed to challenge the earlier accepted nodal $d$-wave pairing in the first unconventional superconductor CeCu$_{2}$Si$_{2}$. Here we obtain multiband Fermi-surface…

The orbital multiplicity in multiband superconductors yields orbital differentiation in normal-state properties, and can lead to orbital-selective spin-fluctuation Cooper pairing. This phenomenon has become increasingly pivotal in…

We consider the minimal two-band model for the Fe-based superconductors with a phenomenological pairing interaction which mimics short-range antiferromagnetic (AFM) fluctuations. Two superconducting (SC) gap solutions are found to exist…

Motivated by exploring superconductivity in multi-orbital systems, we study two orbital models of spinful fermions representing ($p_x,p_y$) or ($d_{xz}, d_{yz})$ orbitals on the square lattice. For minimal interorbital $t$-$J$ or $t$-$V$…

Although the pairing mechanism of the Fe-based superconductors (FeSCs) has not yet been settled with a consensus, as to the pairing symmetry and the superconducting (SC) gap function, the abundant majority of experiments are supporting for…

It is shown that unconventional nature of superconducting state of PrOs_4Sb_12, a Pr-based heavy electron compound with the filled-Skutterudite structure, can be explained in a unified way by taking into account the structure of the…