Based on the two-band tight-binding model composed of the 3d orbital of Ni and the 5d orbital of R (=La), we used the random-phase-approximation method to study the pairing symmetry of the nickelate superconductors. It is found that even without considering the coupling between the R and Ni orbitals, neither the antiferromagnetic spin-fluctuation pattern nor the doping-dependent behavior of the robust d_x²-y²-wave pairing state obtained in our calculations will be obviously influenced. Our results suggest the dominating role of the Ni 3d orbital in determining the low lying physics of the system. Furthermore, our results reveal a dome-shaped doping dependence of the superconducting transition temperature T_c, which is consistent with recent experiments.

The nature of the Cooper pairing in the paradigmatic unconventional superconductor Sr₂RuO₄ is an outstanding puzzle in condensed matter physics. Despite the tremendous efforts made in the past twenty-seven years, neither the pairing symmetry nor the underlying pairing mechanism in this material has been understood with clear consensus. This is largely due to the lack of a superconducting order that is capable of interpreting in a coherent manner the numerous essential experimental observations. At this stage, it may be desirable to reexamine our existing theoretical descriptions of superconducting Sr₂RuO₄. This review focuses on several recent developments that may provide some clues for future study. We highlight three separate aspects: 1) any pairing in the E_u symmetry channel, with which the widely discussed chiral p-wave is associated, shall acquire a 3D structure due to spin-orbit entanglement; 2) if the reported Kerr effect is a superconductivity-induced intrinsic bulk response, the superconductivity must either exhibit a chiral character, or be complex mixtures of certain set of helical p-wave pairings; 3) when expressed in a multiorbital basis, the Cooper pairing could acquire numerous exotic forms that are inaccessible in single-orbital descriptions. The implications of each of these new perspectives are briefly discussed in connection with selected experimental phenomena.

The recent discovery of superconductivity in doped rare-earth infinite-layer nickelates RNiO₂, R=Nd, Pr as a new family of unconventional superconductors has inspired extensive research on their intriguing properties. One of the major motivation to explore the nickelate superconductors originated from their similarities with and differences from the cuprate superconductors, which have been extensively studied over the last decades but are still lack of the thorough understanding. In this short review, we summarized our recent investigation of the relevance of Ni/Cu-3d multiplet structure on the hole doped spin states in cuprate and recently discovered nickelate superconductors via an impurity model incorporating all the 3d orbitals. Further plausible explorations to be conducted are outlined as well. Our presented work provides an insightful framework for the investigation of the strongly correlated electronic systems in terms of the multiplet structure of transition metal compounds.

The last 15 years have witnessed important progresses in our understanding of the mechanism of superconductivity in the high-T_c cuprates. There is now strong evidence that the strange metal behavior is induced by the quantum critical fluctuation at the pseudogap end point, where the Fermi surface changes its topology from hole-like to electron-like. However, experiments show that the quantum critical behavior in the high-T_c cuprates is qualitatively different from that observed in the heavy Fermion systems and the iron-based superconductors, in both of which the quantum critical behavior can be attributed to the quantum phase transition toward a symmetry breaking phase. The fact that the pseudogap exists as a spectral gap without a corresponding symmetry breaking order, together with the fact that the strange metal behavior occurs as a quantum critical behavior without a corresponding symmetry breaking phase transition, exposes the central difficulty of the field: the lack of a universal low energy effective theory description of the high-T_c phenomenology beyond the Landau paradigm. Recent experiments imply that the dualism between the local moment and the itinerant quasiparticle character of the electron in the high-T_c cuprates may serve as an organizing principle to go beyond the Landau paradigm and may hold the key to the mystery of the pseudogap phenomena and the strange metal behavior. It is the purpose of this review to provide an introduction to these recent progresses in the study of the high-T_c cuprate superconductors and their implications on the construction of a coherent picture for the high-T_c problem.

We report the tip-induced superconductivity on the topological semimetal NbSb₂, similar to the observation on TaAs₂ and NbAs₂. Belonging to the same family of MPn₂, all these materials possess similar band structures, indicating that the tip-induced superconductivity may be closely related to their topological nature and share a common mechanism. Further analysis suggests that a bulk band should play the dominant role in such local superconductivity most likely through interface coupling. In addition, the compatibility between the induced superconductivity and tips' ferromagnetism gives an evidence for its unconventional nature. These results provide further clues to elucidate the mechanism of the tip-induced superconductivity observed in topological materials.

We report an inelastic neutron scattering investigation on the spin resonance mode in the optimally hole-doped iron-based superconductor Ba_0.67K_0.33Fe₂As₂ with T_c=38.2 K. Although the resonance is nearly two-dimensional with peak energy E_R≈14 meV, it splits into two incommensurate peaks along the longitudinal direction ([H, 0, 0]) and shows an upward dispersion persisting to 26 meV. Such dispersion breaks through the limit of total superconducting gaps ∆_tot=|∆_k|+|∆_k+Q|(about 11-17 meV) on nested Fermi surfaces measured by high resolution angle resolved photoemission spectroscopy (ARPES). These results cannot be fully understood by the magnetic exciton scenario under s^±-pairing symmetry of superconductivity, and suggest that the spin resonance may not be restricted by the superconducting gaps in the multi-band systems.

This article reviews the basic theoretical aspects of octagraphene, an one-atom-thick allotrope of carbon, with unusual two-dimensional (2D) Fermi nesting, hoping to contribute to the new family of quantum materials. Octagraphene has an almost strongest sp² hybrid bond similar to graphene, and has the similar electronic band structure as iron-based superconductors, which makes it possible to realize high-temperature superconductivity. We have compared various possible mechanisms of superconductivity, including the unconventional s^± superconductivity driven by spin fluctuation and conventional superconductivity based on electron-phonon coupling. Theoretical studies have shown that octagraphene has relatively high structural stability. Although many 2D carbon materials with C₄ carbon ring and C₈ carbon ring structures have been reported, it is still challenging to realize the octagraphene with pure square-octagon structure experimentally. This material holds hope to realize new 2D high-temperature superconductivity.