L’Exil intérieur dans Ulysse

Actes du colloque de Cerisy-la-Salle, 2006International audienc

Constraints from TcT_c and the isotope effect for MgB2_2

With the constraint that $T_c = 39$ K, as observed for MgB$_2$, we use the Eliashberg equations to compute possible allowed values of the isotope coefficient, $\beta$. We find that while the observed value $\beta= 0.32$ can be obtained in principle, it is difficult to reconcile a recently calculated spectral function with such a low observed value

Structural and superconducting transition in selenium under high pressures

First-principles calculations are performed for electronic structures of two high pressure phases of solid selenium, $\beta$-Po and bcc. Our calculation reproduces well the pressure-induced phase transition from $\beta$-Po to bcc observed in selenium. The calculated transition pressure is 30 GPa lower than the observed one, but the calculated pressure dependence of the lattice parameters agrees fairly well with the observations in a wide range of pressure. We estimate the superconducting transition temperature $T_{\rm c}$ of both the $\beta$-Po and the bcc phases by calculating the phonon dispersion and the electron-phonon interaction on the basis of density-functional perturbation theory. The calculated $T_{\rm c}$ shows a characteristic pressure dependence, i.e. it is rather pressure independent in the $\beta$-Po phase, shows a discontinuous jump at the transition from $\beta$-Po to bcc, and then decreases rapidly with increasing pressure in the bcc phase.Comment: 8 pages, 11 figure

Irreducible holonomy algebras of Riemannian supermanifolds

Possible irreducible holonomy algebras \g\subset\osp(p,q|2m) of Riemannian supermanifolds under the assumption that \g is a direct sum of simple Lie superalgebras of classical type and possibly of a one-dimensional center are classified. This generalizes the classical result of Marcel Berger about the classification of irreducible holonomy algebras of pseudo-Riemannian manifolds.Comment: 27 pages, the final versio

First-Principles Calculation of the Superconducting Transition in MgB2 within the Anisotropic Eliashberg Formalism

We present a study of the superconducting transition in MgB2 using the ab-initio pseudopotential density functional method and the fully anisotropic Eliashberg equation. Our study shows that the anisotropic Eliashberg equation, constructed with ab-initio calculated momentum-dependent electron-phonon interaction and anharmonic phonon frequencies, yields an average electron-phonon coupling constant lambda = 0.61, a transition temperature Tc = 39 K, and a boron isotope-effect exponent alphaB = 0.31 with a reasonable assumption of mu* = 0.12. The calculated values for Tc, lambda, and alphaB are in excellent agreement with transport, specific heat, and isotope effect measurements respectively. The individual values of the electron-phonon coupling lambda(k,k') on the various pieces of the Fermi surface however vary from 0.1 to 2.5. The observed Tc is a result of both the raising effect of anisotropy in the electron-phonon couplings and the lowering effect of anharmonicity in the relevant phonon modes.Comment: 4 pages, 3 figures, 1 tabl

Anomalous roughening of wood fractured surfaces

Scaling properties of wood fractured surfaces are obtained from samples of three different sizes. Two different woods are studied: Norway spruce and Maritime pine. Fracture surfaces are shown to display an anomalous dynamic scaling of the crack roughness. This anomalous scaling behavior involves the existence of two different and independent roughness exponents. We determine the local roughness exponents ${\zeta}_{loc}$ to be 0.87 for spruce and 0.88 for pine. These results are consistent with the conjecture of a universal local roughness exponent. The global roughness exponent is different for both woods, $\zeta$ = 1.60 for spruce and $\zeta$ = 1.35 for pine. We argue that the global roughness exponent $\zeta$ is a good index for material characterization.Comment: 7 two columns pages plus 8 ps figures, uses psfig. To appear in Physical Review

The Morphology of N=6 Chern-Simons Theory

We tabulate various properties of the language of N=6 Chern-Simons Theory, in the sense of Polyakov. Specifically we enumerate and compute character formulas for all syllables of up to four letters, i.e. all irreducible representations of OSp(6|4) built from up to four fundamental fields of the ABJM theory. We also present all tensor product decompositions for up to four singletons and list the (cyclically invariant) four-letter words, which correspond to single-trace operators of length four. As an application of these results we use the two-loop dilatation operator to compute the leading correction to the Hagedorn temperature of the weakly-coupled planar ABJM theory on R \times S^2.Comment: 41 pages, 1 figure; v2: minor correction

Isotope Effect in the Presence of Magnetic and Nonmagnetic Impurities

The effect of impurities on the isotope coefficient is studied theoretically in the framework of Abrikosov-Gor'kov approach generalized to account for both potential and spin-flip scattering in anisotropic superconductors. An expression for the isotope coefficient as a function of the critical temperature is obtained for a superconductor with an arbitrary contribution of spin-flip processes to the total scattering rate and an arbitrary degree of anisotropy of the superconducting order parameter, ranging from isotropic s-wave to d-wave and including anisotropic s-wave and mixed (s+d)-wave as particular cases. It is found that both magnetic and nonmagnetic impurities enhance the isotope coefficient, the enhancement due to magnetic impurities being generally greater than that due to nonmagnetic impurities. From the analysis of the experimental results on La-Sr-Cu-M-O high temperature superconductor, it is concluded that the symmetry of the pairing state in this system differs from a pure d-wave.Comment: 4 pages, 3 figure

The polaron-like nature of an electron coupled to phonons

When an electron interacts with phonons, the electron can exhibit either free electron-like or polaron-like properties. The latter tends to occur for very strong coupling, and results in a phonon cloud accompanying the electron as it moves, thus raising its mass considerably. We summarize this behaviour for the Holstein model in one, two and three dimensions, and note that the crossover occurs for fairly low coupling strengths compared to those attributed to real materials exhibiting conventional superconductivity.Comment: 5 pages; contains a summary of single particle results for the Holstein mode

The 3-Band Hubbard-Model versus the 1-Band Model for the high-Tc Cuprates: Pairing Dynamics, Superconductivity and the Ground-State Phase Diagram

One central challenge in high-$T_c$ superconductivity (SC) is to derive a detailed understanding for the specific role of the $Cu$-$d_{x^2-y^2}$ and $O$-$p_{x,y}$ orbital degrees of freedom. In most theoretical studies an effective one-band Hubbard (1BH) or t-J model has been used. Here, the physics is that of doping into a Mott-insulator, whereas the actual high-$T_c$ cuprates are doped charge-transfer insulators. To shed light on the related question, where the material-dependent physics enters, we compare the competing magnetic and superconducting phases in the ground state, the single- and two-particle excitations and, in particular, the pairing interaction and its dynamics in the three-band Hubbard (3BH) and 1BH-models. Using a cluster embedding scheme, i.e. the variational cluster approach (VCA), we find which frequencies are relevant for pairing in the two models as a function of interaction strength and doping: in the 3BH-models the interaction in the low- to optimal-doping regime is dominated by retarded pairing due to low-energy spin fluctuations with surprisingly little influence of inter-band (p-d charge) fluctuations. On the other hand, in the 1BH-model, in addition a part comes from "high-energy" excited states (Hubbard band), which may be identified with a non-retarded contribution. We find these differences between a charge-transfer and a Mott insulator to be renormalized away for the ground-state phase diagram of the 3BH- and 1BH-models, which are in close overall agreement, i.e. are "universal". On the other hand, we expect the differences - and thus, the material dependence to show up in the "non-universal" finite-T phase diagram ($T_c$-values).Comment: 17 pages, 9 figure