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Inspired by the recent discovery of a successive evolutions of electronically ordered states, we present a self-consistent theoretical analysis that treats the interactions responsible for the chiral charge order and superconductivity on an equal footing. It is revealed that the self-consistent theory captures the essential features of the successive temperature evolutions of the electronic states from the high-temperature ``triple-$Q$" $2\times 2$ charge-density-wave state to the nematic charge-density-wave phase, and finally to the low-temperature superconducting state coexisting with the nematic charge density wave. We provide a comprehensive explanation for the temperature evolutions of the charge ordered states and discuss the consequences of the intertwining of the superconductivity with the nematic charge density wave. Our findings not only account for the successive temperature evolutions of the ordered electronic states discovered in experiments but also provide a natural explanation for the two-fold rotational symmetry observed in both the charge-density-wave and superconducting states. Moreover, the intertwining of the superconductivity with the nematic charge density wave order may also be an advisable candidate to reconcile the divergent or seemingly contradictory experimental outcomes regarding the superconducting properties.

Motivated by recent experimental evidences signalling the chiral charge order in the vanadium-based kagome superconductors, we theoretically investigate the impact of the chiral flux charge order over the experimental outcomes for the normal and the SC properties. It is revealed that the spectral weight on the Fermi surface (FS) is partially gaped by the chiral flux charge order with the reservation of the spectral weight on the $M$ points and the midpoint between the two adjacent $M$ points, resulting in the momentum-dependent energy gap being consistent with the recent experimental observations. More importantly, by considering the influence of the chiral flux charge order, we find that a conventional fully gapped SC pairing state evolves into a nodal gap feature for the spectral weight due to the spectral gap modulations on the FS. As a result, the U-shaped density of states (DOS) deforms to the V-shaped one along with the residual DOS near the Fermi energy. These results bear some resemblance to the experimental observations, and may serve as a promising proposal to mediate the divergent or seemingly contradictory experimental outcomes about the SC pairing symmetry.

Starting from a tight-binding model on the kagome lattice near the van Hove filling, the superconducting (SC) properties are investigated self-consistently using the Bogoliubov-de Gennes equation with the consideration of the inequivalent third-neighbor (TN) bonds. Near the van Hove filling, the most favorable SC pairings are found to derive from the electrons belonging to the same sublattice sites, including the on-site $s$-wave and the spin-singlet/triplet TN pairings. The inequivalent TN bonds will result in multiple SC components with different orbital angular momentums (OAM) for the TN SC pairings. While the density of states (DOS) and the temperature ($T$) dependence of the spin-lattice relaxation rate ($T^{-1}_{1}$) exhibit distinct line shapes in the SC state for the three cases, a peak structure in the $T$ dependence of $T^{-1}_{1}$ can be found for both cases just below $T_{c}$ as a result of the van Hove singularity, even though the SC gap has nodes. The effects of magnetic vortices on the low energy excitations and on the $T$ dependence of $T^{-1}_{1}$ with the implications of the results are also discussed for both cases., Comment: 9 pages, 4 figures, 2 tables

Ising spin-orbital coupling is usually easy to identify in the Ising superconductors via an in-plane critical field enhancement, but we show that the Ising spin-orbital coupling also manifests in the vortex physics for perpendicular magnetic fields. By self-consistently solving the Bogoliubov-de Gennes equations of a model Hamiltonian built on the honeycomb lattice with the Ising spin-orbital coupling pertinent to the transition metal dichalcogenides, we numerically investigate the local breaking of the spin and sublattice degeneracies in the presence of a perpendicular magnetic field. It is revealed that the ferromagnetic orders are induced inside the vortex core region by the Ising spin-orbital coupling. The induced magnetic orders are antiphase in terms of their opposite polarizations inside the two nearest-neighbor vortices with one of the two polarizations coming dominantly from one sublattice sites, implying the local breaking of the spin and sublattice degeneracies. The finite-energy peaks of the local-density-of-states for spin-up and spin-down in-gap states are split and shifted oppositely by the Ising spin-orbital coupling, and the relative shifts of them on sublattices $A$ and $B$ are also of opposite algebraic sign. The calculated results and the proposed scenario may not only serve as experimental signatures for identifying the Ising spin-orbital coupling in the Ising superconductors, but also be prospective in manipulation of electron spins in motion through the orbital effect in the superconducting vortex states., Comment: 9 pages, 5figures

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 ordering 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 $d_{x^2-y^2} \pm d_{3z^2-r^2}$., Comment: published version

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., Comment: 6 pages, 5 figures

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 experiment 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., Comment: 6 pages, 6 figures

The effects of magnetic vortices and nonmagnetic impurities on the low energy quasiparticle excitations and the spin-lattice relaxation rate are examined in the iron-based superconductors for the $s_{\pm}$-, $s$- and d-wave pairing symmetries, respectively. The main effect of the vortices is to enhance the quasiparticle excitations and the spin-lattice relaxation rate for all symmetries, and leads to a $T^{3}$ dependence of the relaxation rate followed by a nearly $T$-linearity at lower temperatures. This enhancement can only be seen for the $s_{\pm}$- and d-wave symmetries in the presence of nonmagnetic impurities. These results suggest that the $s_{\pm}$-wave and d-wave pairing states behave similarly in response to the magnetic field and nonmagnetic impurities, therefore it may be impossible to distinguish them on the basis of the measurements of spin-lattice relaxation rates when a magnetic field and/or impurity scatterings are present., Comment: 7 pages, 5 figures

In the framework of the slave-boson approach to the $t-t'-t''-J$ model, it is found that for electron-doped high-$T_c$ cuprates, the staggered antiferromagnetic (AF) order coexists with superconducting (SC) order in a wide doping level ranged from underdoped to nearly optimal doping at the mean-field level. In the coexisting phase, it is revealed that the spin response is commensurate in a substantial frequency range below a crossover frequency $\omega_{c}$ for all dopings considered, and it switches to the incommensurate structure when the frequency is higher than $\omega_{c}$. This result is in agreement with the experimental measurements. Comparison of the spin response between the coexisting phase and the pure SC phase with a $d_{x^{2}-y^{2}}$-wave pairing plus a higher harmonics term (DP+HH) suggests that the inclusion of the two-band effect is important to consistently account for both the dispersion of the spin response and the non-monotonic gap behavior in the electron-doped cuprates., Comment: 6 pages, 5 figures

Magnetism in the FeAs stoichiometric compounds and its interplay with superconductivity in vortex states are studied by self-consistently solving the BdG equations based on a two-orbital model with including the on-site interactions between electrons in the two orbitals. It is revealed that for the parent compound, magnetism is caused by the strong Hund's coupling, and the Fermi surface topology aids to select the spin-density-wave (SDW) pattern. The superconducting (SC) order parameter with $s_{\pm}=\Delta_{0}\cos(k_{x})\cos(k_{y})$ symmetry is found to be the most favorable pairing for both the electron- and hole-doped cases, while the local density-of-states (LDOS) exhibits the characteristic of nodal gap for the former and full gap for the latter. In the vortex state, the emergence of the field-induced SDW depends on the strength of the Hund's coupling and the Coulomb repulsions. The field-induced SDW gaps the finite energy contours on the electron and hole pocket sides, leading to the dual structures with one reflecting the SC pairing and the other being related to the SDW order. These features can be discernable in STM measurements for identifying the interplay between the field-induced SDW order and the SC order around the core region., Comment: 8 pages

We investigate the superconducting order parameter, the spectral and optical properties in a stripe model with spin (charge) domain-derived scattering potential $V_{s}$ ($V_{c}$). We show that the charge domain-derived scattering is less effective than the spin scattering on the suppression of superconductivity. For $V_{s}\gg V_{c}$, the spectral weight concentrates on the ($\pi,0$) antinodal region, and a finite energy peak appears in the optical conductivity with the disappearance of the Drude peak. But for $V_{s}\approx V_{c}$, the spectral weight concentrates on the ($\pi/2,\pi/2$) nodal region, and a residual Drude peak exists in the optical conductivity without the finite energy peak. These results consistently account for the divergent observations in the ARPES and optical conductivity experiments in several high-$T_c$ cuprates, and suggest that the "insulating" and "metallic" properties are intrinsic to the stripe state, depending on the relative strength of the spin and charge domain-derived scattering potentials., Comment: 7 pages, 4 figures