Superconductivity in multi-band and disordered systems

In the first part, we explain the properties of the normal state of iron-pnictides, the pairing mechanism of superconductivity and experimental detection of pairing symmetry. The quasi two dimensional tri-layers consisting of iron and arsenic play the key role in iron-pnictides. Experimentally, structural phase transition (SPT) from a tetragonal crystal to orthorhombic one, resistivity anomaly (RA) and phase transition to stripe-like antiferromagnetic order with small staggered magnetic moments are three common features of iron-pncitides. The SPT is attributed to the Jahn-Teller effect. Due to the anisotropy in the xy plane of the dxz, and dyz orbitals of the iron atoms, orbital ordering will make the orthorhombic structure more energetically favorable, thus inducing the SPT. In an orbital ordered system, the sites with orbitals that do not order will act as scattering impurities, causing a RA upon the onset of the SPT. In addition, the combined effects of spin-orbit, monoclinic distortion, and p-d hybridization of Fe in LaFeAsO invalidates the naive Hund's rule filling of the Fe d-levels. The two highest occupied levels have one electron each but as a result of differing p-d hybridizations, the upper level is more itinerant while electrons in the lower level are more localized. We call this the itinerant-localized dichotomous model. The screening of localized magnetic moment by itinerant electrons explains the small magnetic moment in this material.;The pairing mechanism of superconductivity is related to the multi-band properties of iron-pnictides. Itinerant electrons form four Fermi surfaces: two hole Fermi surfaces centered on (0, 0) and two electronic Fermi surfaces centered on (pi,pi) in momentum space. Itinerant electrons on the Fermi surfaces interact with each other by propagating magnons induced by localized electrons. The induced inter-Fermi-surface interactions dominate intra-Fermi-surface interactions. Although both interactions are repulsive, a superconductivity state emerges in which the order parameter on each Fermi surface is s-wave and changes sign between Fermi surfaces sheets. We call such a state s+/-. Finally, we propose a modified Josephson corner-junction experiment to test this prediction.;The second part is devoted to superconductivity in disordered systems. Two problems are treated: (1) the metallic state that intervenes between the transition from the superconductor to an insulator in thin 2D metal alloy films, (2) supersolidity in 4He.;Disorder will induce an intermediate state in the superconductor-insulator transition which is the so-called Bose metal. Using the disordered quantum rotor model, we analyze the transport properties in the vicinity of the multicritical point between the superconductor, Bose metal and insulating phases. We find that a magnetic field leaves metallic transport of bosons in the glassy phase in tact. In the vicinity of the superconductivity-to-Bose metal transition, the resistitivy turns on as (H - Hc) 2 with Hc. The metallic state is also shown to persist in three spatial dimensions. As the phase glass in d = 3 is identical to the vortex glass, we conclude that the vortex glass is, in actuality, a metal rather than a superconductor at T = 0.;We propose that a clean array 4He atoms is a self-generated Mott insulator, that is, the 4He atoms constitute the lattice as well as the charge carriers. With this assumption, we are able to interpret the textbook defect-driven supersolids as excitations of either the lower or upper Hubbard bands. In the experiments at hand, disorder induces a closing of the Mott gap through the generation of mid-gap localized states at the chemical potential. Depending on the magnitude of the disorder, we find that the destruction of the Mott state takes place for d + z > 4 either through a Bose glass phase (strong disorder) or through a direct transition to a superfluid (weak disorder). For d + z < 4, disorder is always relevant. The critical value of the disorder that separates these two regimes is shown to be a function of the boson filling, interaction and the momentum cut off. We apply our work to the experimentally observed enhancement 3He impurities has on the onset temperature for the missing moment of inertia. We find quantitative agreement with experimental trends. (Abstract shortened by UMI.)...