Superconductivity with hard-core repulsion: BCS-Bose crossover and s-/d-wave competition

We consider fermions on a 2D lattice interacting repulsively on the same site and attractively on the nearest neighbor sites. The model is relevant, for instance, to study the competition between antiferromagnetism and superconductivity in a Kondo lattice. We first solve the two-body problem to show that in the dilute and strong coupling limit the s-wave Bose condensed state is always the ground state. We then consider the many-body problem and treat it at mean-field level by solving exactly the usual gap equation. This guarantees that the superconducting wave-function correctly vanishes when the two fermions (with antiparallel spin) sit on the same site. This fact has important consequences on the superconducting state that are somewhat unusual. In particular this implies a radial node-line for the gap function. When a next neighbor hopping t' is present we find that the s-wave state may develop nodes on the Fermi surface.Comment: 10 pages, 9 fig

Effective field theories for correlated electrons

In this thesis, techniques of functional integration are applied to the construction of effective field theories for models of strongly correlated electrons. This is accomplished by means of the Hubbard-Stratonovic transformation which maps a system of interacting fermions onto one of free fermions interacting, not with each other, but with bosonic fields representing the collective modes of the system. Different choices of transformation are investigated throughout the thesis. It is shown that there exists a new group of discrete symmetries and transformations of the Hubbard model. Using this new group, the problem of choosing a Hubbard-Stratonovic decomposition of the Hubbard interaction term is solved. In the context of the exotic doped barium bismuthates, an extended Hubbard model with on-site attraction and nearest neighbour repulsion is studied. Mean field and renormalisation group analyses show a 'pseudospin-flop' from charge density wave to superconductivity as a function of filling. The nearest neighbour attractive Hubbard model on a quasi-2D lattice is studied as a simple phenomenological model for the high-T_c cuprates. Mean field theory shows a transition from pure d-wave to pure s-wave superconductivity, via a mixed symmetry s + id state. Using Gaussian fluctuations, the BCS-Bose crossover is examined and suggestions are made about the origin of the angle dependence of the pseudogap. The continuum delta-shell potential model is introduced for anisotropic superconductors. Its mean field phases are studied and found to have some unusual properties. The BCS-Bose crossover is examined and the results are compared with those of the lattice model. Quasi-2D (highly anisotropic 3D) systems are considered. The critical properties of a Bose gas are investigated as the degree of anisotropy is varied. A new 2D Bose condensate state is found. A renormalisation group analysis is used to investigate the crossover from 2D to 3D. (author)Available from British Library Document Supply Centre-DSC:DXN028028 / BLDSC - British Library Document Supply CentreSIGLEGBUnited Kingdo

Atmospheric emissions and attenuation of non-methane organic compounds in cover soils at a French landfill

In addition to methane (CH(4)) and carbon dioxide (CO(2)), landfill gas may contain more than 200 non-methane organic compounds (NMOCs) including C(2+)-alkanes, aromatics, and halogenated hydrocarbons. Although the trace components make up less than 1% v/v of typical landfill gas, they may exert a disproportionate environmental burden. The objective of this work was to study the dynamics of CH(4) and NMOCs in the landfill cover soils overlying two types of gas collection systems: a conventional gas collection system with vertical wells and an innovative horizontal gas collection layer consisting of permeable gravel with a geomembrane above it. The 47 NMOCs quantified in the landfill gas samples included primarily alkanes (C(2)-C(10)), alkenes (C(2)-C(4)), halogenated hydrocarbons (including (hydro)chlorofluorocarbons ((H)CFCs)), and aromatic hydrocarbons (BTEXs). In general, both CH(4) and NMOC fluxes were all very small with positive and negative fluxes. The highest percentages of positive fluxes in this study (considering all quantified species) were observed at the hotspots, located mainly along cell perimeters of the conventional cell. The capacity of the cover soil for NMOC oxidation was investigated in microcosms incubated with CH(4) and oxygen (O(2)). The cover soil showed a relatively high capacity for CH(4) oxidation and simultaneous co-oxidation of the halogenated aliphatic compounds, especially at the conventional cell. Fully substituted carbons (TeCM, PCE, CFC-11, CFC-12, CFC-113, HFC-134a, and HCFC-141b) were not degraded in the presence of CH(4) and O(2). Benzene and toluene were also degraded with relative high rates. This study demonstrates that landfill soil covers show a significant potential for CH(4) oxidation and co-oxidation of NMOCs