Abstract:
We present a theoretical description of the London penetration depth of a multi-band superconductor in the case when both superconducting and spin-density wave orders coexist. We focus on clean systems and zero temperature to emphasize the effect of the two competing orders. Our calculation shows that the supefluid density closely follows the evolution of the superconducting order parameter as doping is increased, saturating to a BCS value in the pure superconducting state. Furthermore, we predict a strong anisotropic in-pane penetration depth induced by the spin-density wave order.

Abstract:
In a recent inelastic neutron scattering experiment in the pseudogap state of the high temperature superconductor $\mathrm{YBa_{2}Cu_{3}O_{6.6}}$ an unusual `vertical' dispersion of the spin excitations with a large in-plane anisotropy was observed. In this paper we discuss in detail the spin susceptibility of the singlet $d$-density wave, the triplet $d$-density wave, as well as the more common spin density wave orders with hopping anisotropies. From numerical calculations within the framework of random phase approximation, we find nearly vertical dispersion relations for spin excitations with anisotropic incommensurability at low energy $\omega \le 90 meV$, which are reminiscent of the experiments. At very high energy $\omega \ge 165 meV$, we also find energy-dependent incommensurability. Although there are some important difference between the three cases, unpolarized neutron measurements cannot discriminate between these alternate possibilities; the vertical dispersion, however, is a distinct feature of all three density wave states in contrast to the superconducting state, which shows an hour-glass shape dispersion.

Abstract:
Coexistence of antiferromagnetic order with superconductivity in many families of newly discovered iron-based superconductors has renewed interest to this old problem. Due to competition between the two types of order, one can expect appearance of the antiferromagnetism inside the cores of the vortices generated by the external magnetic field. The structure of a vortex in type II superconductors holds significant importance from the theoretical and the application points of view. Here we consider the internal vortex structure in a two-band s$_\pm$ superconductor near a spin-density-wave instability. We treat the problem in a completely self-consistent manner within the quasiclassical Eilenberger formalism. We study the structure of the s$_\pm$ superconducting order and magnetic field-induced spin-density-wave order near an isolated vortex. We examine the effect of this spin-density-wave state inside the vortex cores on the local density of states.

Abstract:
We investigate the emergent impurity-induced states arising from point-like scatterers in the spin-density wave phase of iron-based superconductors within a microscopic five-band model. Independent of the details of the band-structure and disorder potential, it is shown how stable magnetic (pi,pi) unidirectional nematogens are formed locally by the impurities. Interestingly, these nematogens exhibit a dimer structure in the electronic density, are directed along the antiferromagnetic a-axis, and have typical lengths of order 10 lattice constants in excellent agreement with recent scanning tunnelling experiments. These electronic dimers provide a natural explanation of the dopant-induced transport anisotropy found e.g. in the 122 iron pnictides.

Abstract:
The quasiparticle states around a nonmagnetic impurity in electron-doped iron-based superconductors with spin-density-wave (SDW) order are investigated as a function of doping and impurity scattering strength. In the undoped sample, where a pure SDW state exists, two impurity-induced resonance peaks are observed around the impurity site and they are shifted to higher (lower) energies as the strength of the positive (negative) scattering potential (SP) is increased. For the doped samples where the SDW order and the superconducting order coexist, the main feature is the existence of sharp in-gap resonance peaks whose positions and intensity depend on the strength of the SP and the doping concentration. In all cases, the local density of states exhibits clear $C_2$ symmetry. We also note that in the doped cases, the impurity will divide the system into two sublattices with distinct values of magnetic order. Here we use the band structure of a two-orbital model, which considers the asymmetry of the As atoms above and below the Fe-Fe plane. This model is suitable to study the properties of the surface layers in the iron-pnictides and should be more appropriate to describe the scanning tunneling microscopy experiments.

Abstract:
Elucidating the nature of the magnetic ground state of iron-based superconductors is of paramount importance in unveiling the mechanism behind their high temperature superconductivity. Until recently, it was thought that superconductivity emerges only from an orthorhombic antiferromagnetic stripe phase, which can in principle be described in terms of either localized or itinerant spins. However, we recently reported that tetragonal symmetry is restored inside the magnetically ordered state of a hole-doped BaFe2As2. This observation was interpreted as indirect evidence of a new double-Q magnetic structure, but alternative models of orbital order could not be ruled out. Here, we present Mossbauer data that show unambiguously that half of the iron sites in this tetragonal phase are non-magnetic, establishing conclusively the existence of a novel magnetic ground state with a non-uniform magnetization that is inconsistent with localized spins. We show that this state is naturally explained as the interference between two spin-density waves, demonstrating the itinerant character of the magnetism of these materials and the primary role played by magnetic over orbital degrees of freedom.

Abstract:
A novel spin density wave (SDW) instability mechanism enhanced by vortices under fields is proposed to explain the high field and low temperature (HL) phase in CeCoIn$_5$. In the vortex state the strong Pauli effect and the nodal gap conspire to enhance the momentum resolved spectral weight exclusively along the nodal direction over the normal value, providing a favorable nesting condition for SDW with ${\bf Q}=(2k_F, 2k_F, 0.5)$ only under high field ($H$). Observed mysteries of the field-induced SDW confined within $H_{c2}$ are understood consistently, such facts that ${\bf Q}$ is directed to the nodal direction independent of $H$, SDW diminishes under tilting field from the $ab$ plane, and the SDW transition line in $(H,T)$ has a positive slope.

Abstract:
We present a theory of the pinning of dynamic spin density wave (SDW) fluctuations in a d-wave superconductor by local imperfections which preserve spin-rotation invariance, such as impurities or vortex cores. The pinning leads to static spatial modulations in spin-singlet observables, while the SDW correlations remain dynamic: these are the `Friedel oscillations' of a spin-gap antiferromagnet. We connect the spectrum of these modulations as observed by scanning tunnelling microscopy to the dynamic spin structure factor measured by inelastic neutron scattering.

Abstract:
The spin density wave and its temperature dependence in oxypnictide are studied in a three-band model. The spin susceptibilities with various interactions are calculated in the random phase approximation(PPA). It is found that the spin susceptibility peaks around the M point show a spin density wave(SDW) with momentum (0, $\pi$) and a clear stripe-like spin configuration. The intra-band Coulomb repulsion enhances remarkably the SDW but the Hund's coupling weakens it. It is shown that a new resonance appears at higher temperatures at the $\Gamma$ point indicating the formation of a paramagnetic phase. There is a clear transition from the SDW phase to the paramagnetic phase.

Abstract:
Using a simple model of multi-band superconductors, which can be applied in particular to Fe\nobreakdash-based pnictides, we calculate the Josephson current $I_{\text{J}}$ in a tunnel junction composed by such superconductors. We employ the tunneling Hamiltonian method and quasiclassical Green's functions. We study both the case of coexistence of the superconducting ($\Delta $) and magnetic (SDW---spin density wave) order parameters and the case when only the superconducting order parameter exists. We show that the current $I_{\text{J}}$ depends on the mutual orientation of magnetization of the SDW in the case of non-ideal nesting when the coexistence of superconducting and magnetic order parameters is possible as it takes place in Fe\nobreakdash-based pnictides. It is found that the realization of the $\pi$\nobreakdash-junction is possible in both cases. We compare our results for multi-band superconductors without the SDW with those obtained earlier and find that they coincide if the tunneling matrix elements are real. If these elements are complex, a new term appears in the formula for the Josephson critical current.