We investigate the pairing symmetry in heavily overdoped Ba$_{1-x}$K$_{x}$Fe$_{2}$As$_{2}$ based on the spin-fluctuation mechanism. The exotic octet nodes of the superconducting gap and the unusual evolution of the gap with doping observed by the rec
ent experiments are well explained in a unified manner. We demonstrate that the scatterings of electrons on the Fermi patches is mainly responsible for the incommensurate spin fluctuations and consequently the Fermi-surface-dependent multi-gap structure, since the Fermi level is close to the flat band. In addition, we find that a $d$-wave pairing state will prevail over the s-wave pairing state around the Lifshitz transition point.
We investigate the high temperature phase of layered manganites, and demonstrate that the charge-orbital phase transition without magnetic order in La$_{0.5}$Sr$_{1.5}$MnO$_4$ can be understood in terms of the density wave instability. The orbital or
dering is found to be induced by the nesting between segments of Fermi surface with different orbital characters. The simultaneous charge and orbital orderings are elaborated with a mean field theory. The ordered orbitals are shown to be $d_{x^2-y^2} pm d_{3z^2-r^2}$.
We report theoretical and experimental studies of the effect of Zn-impurity in Fe-based superconductors. Zn-impurity is expected to severely suppress sign reversed s$_pm$ wave pairing. The experimentally observed suppression of T$_c$ under Zn-doping
strongly depends on the materials and the charge carrier contents, which suggests competition of $s_{++}$ and $s_{pm}$ pairings in Fe-base superconductors. We study a model incorporating both $s_{++}$ and $s_{pm}$ pairing couplings by using Bogoliubov de-Gennes equation, and show that the Zn-impurity strongly suppresses $s_{pm}$ pairing and may induce a transition from $s_{pm}$ to $s_{++}$-wave. Our theory is consistent with various experiments on the impurity effect. We present new experimental data on the Zn-doping SmFe$_{1-x}$Zn$_x$AsO$_{0.9}$F$_{0.1}$ of T$_c=$ 50K, in further support of our proposal.
We study the effect of a single non-magnetic impurity in A$_{y}$Fe$_{2-x}$Se$_{2}$ (A=K, Rb, or Cs) superconductors by considering various pairing states based on a three-orbital model consistent with the photoemission experiments. The local density
of states on and near the impurity site has been calculated by solving the Bogoliubov-de Gennes equations self-consistently. The impurity-induced in-gap bound states are found only for attractive impurity scattering potential, as in the cases of doping of Co or Ni, which is characterized by the strong particle-hole asymmetry, in the nodeless $d_{x^2-y^2}$ wave pairing state. This property may be used to probe the pairing symmetry of FeSe-based 122-type superconductors.
Recent transport experiments have demonstrated that the rhombohedral stacking trilayer graphene is an insulator with an intrinsic gap of 6meV and the Bernal stacking trilayer one is a metal. We propose a Hubbard model with a moderate $U$ for layered
graphene sheets, and show that the model well explains the experiments of the stacking dependent energy gap. The on-site Coulomb repulsion drives the metallic phase of the non-interacting system to a weak surface antiferromagnetic insulator for the rhombohedral stacking layers, but does not alter the metallic phase for the Bernal stacking layers.
Recent discovery of superconducting (SC) ternary iron selenides has block antiferromagentic (AFM) long range order. Many experiments show possible mesoscopic phase separation of the superconductivity and antiferromagnetism, while the neutron experime
nt reveals a sizable suppression of magnetic moment due to the superconductivity indicating a possible phase coexistence. Here we propose that the observed suppression of the magnetic moment may be explained due to the proximity effect within a phase separation scenario. We use a two-orbital model to study the proximity effect on a layer of block AFM state induced by neighboring SC layers via an interlayer tunneling mechanism. We argue that the proximity effect in ternary Fe-selenides should be large because of the large interlayer coupling and weak electron correlation. The result of our mean field theory is compared with the neutron experiments semi-quantitatively. The suppression of the magnetic moment due to the SC proximity effect is found to be more pronounced in the d-wave superconductivity and may be enhanced by the frustrated structure of the block AFM state.
Based on an effective two-band model and using the fluctuation-exchange (FLEX) approach, we explore spin fluctuations and unconventional superconducting pairing in Fe-based layer superconductors. It is elaborated that one type of interband antiferrom
agnetic (AF) spin fluctuation stems from the interband Coulomb repulsion, while the other type of intraband AF spin fluctuation originates from the intraband Coulomb repulsion. Due to the Fermi-surface topology, a spin-singlet extended s-wave superconducting state is more favorable than the nodal $d_{XY}$-wave state if the interband AF spin fluctuation is more significant than the intraband one, otherwise vice versa. It is also revealed that the effective interband coupling plays an important role in the intraband pairings, which is a distinct feature of the present two-band system.
Based on a single band Hubbard model and the fluctuation exchange approximation, the effective mass and the energy band renormalization in Na$_{0.33}$CoO$_2$ is elaborated. The renormalization is observed to exhibit certain kind of anisotropy, which
agrees qualitatively with the angle-resolved photoemission spectroscopy (ARPES) measurements. Moreover, the spectral function and density of states (DOS) in the normal state are calculated, with a weak pseudogap behavior being seen, which is explained as a result of the strong Coulomb correlations. Our results suggest that the large Fermi surface (FS) associated with the $a_{1g}$ band plays likely a central role in the charge dynamics.
