We investigate the effects of (Curvature) 2 -and (Torsion) 2 -terms in the Einstein-Hilbert-Chern-Simons Lagrangian. The purposes are two-fold: (i) to show the efficacy of an orthogonal basis of degree-of-freedom projection operators recently proposed and to ascertain its adequacy for obtaining propagators of general parity-breaking gravity models in three dimensions; (ii) to analyze the role of the topological Chern-Simons term for the unitarity and the particle spectrum of the model squared-curvature terms in connection with dynamical torsion. Our conclusion is that the Chern-Simons term does not influence the unitarity conditions imposed on the parameters of the Lagrangian, but significantly modifies the particle spectrum. * Electronic address: helayel@cbpf.br † Electronic address: carlos@cbpf.br ‡ Electronic address: bpdias@cbpf.br § Electronic address: alfredov@cbpf.br ¶ Electronic address: vjose@cbpf.br

We present two different versions of the consistent theory of massive gravitons in arbitrary space-times which are simple enough for practical applications. The theory is described by a non-symmetric rank-2 tensor whose equations of motion imply six algebraic and five differential constraints reducing the number of independent components to five. The theory reproduces the standard description of massive gravitons in Einstein spaces. In generic spacetimes it does not show the massless limit and always propagates five degrees of freedom, even for the vanishing mass parameter. We illustrate these features by an explicit calculation for a homogeneous and isotropic cosmological background. We find that the gravitons are stable if they are sufficiently massive, hence they may be a part of Dark Matter at present. We discuss also other possible applications.

We analyze the paradigmatic competition between intra-band and cross-band Cooper-pair formation in two-band superconductors, neglected in most works to date. We derive the phase-sensitive gap equations and describe the crossover between the intraband-dominated and the crossbanddominated regimes, delimited by a "gapless" state. Experimental signatures of crosspairing comprise notable gap-splitting in the excitation spectrum, non-BCS behavior of gaps versus temperature, as well as changes in the pairing symmetry as a function of temperature. The consequences of these findings are illustrated on the examples of MgB2 and Ba0.6K0.4Fe2As2.

Ultrathin superconductors of different materials are becoming a powerful platform to find mechanisms for enhancement of superconductivity, exploiting shape resonances in different superconducting properties. Here we evaluate the superconducting gap and its spatial profile, the multiple gap components, and the chemical potential, of generic superconducting nanofilms, considering the pairing attraction and its energy scale as tunable parameters, from weak to strong coupling, at fixed electron density. Superconducting properties are evaluated at mean field level as a function of the thickness of the nanofilm, in order to characterize the shape resonances in the superconducting gap. We find that the most pronounced shape resonances are generated for weakly coupled superconductors, while approaching the strong coupling regime the shape resonances are rounded by a mixing of the subbands due to the large energy gaps extending over large energy scales. Finally, we find that the spatial profile, transverse to the nanofilm, of the superconducting gap acquires a flat behavior in the shape resonance region, indicating that a robust and uniform multigap superconducting state can arise at resonance.