Theory of High-Tc Superconducting Cuprates Based on Experimental Evidence

A model of superconductivity in layered high-temperature superconducting cuprates is proposed, based on the extended saddle point singularities in the electron spectrum, weak screening of the Coulomb interaction and phonon-mediated interaction between electrons plus a small short -range repulsion of Hund's, or spin-fluctuation, origin. This permits to explain the large values of $Tc$, features of the isotope effect on oxygen and copper, the existence of two types of the order parameter, the peak in the inelastic neutron scattering, the positive curvature of the upper critical field, as function of temperature etc.Comment: RevTeX 3.x, 11 Postscript figures (included); send comments to [email protected]

Habitable planets around the star Gl 581?

Radial velocity surveys are now able to detect terrestrial planets at habitable distance from M-type stars. Recently, two planets with minimum masses below 10 Earth masses were reported in a triple system around the M-type star Gliese 581. Using results from atmospheric models and constraints from the evolution of Venus and Mars, we assess the habitability of planets Gl 581c and Gl 581d and we discuss the uncertainties affecting the habitable zone (HZ) boundaries determination. We provide simplified formulae to estimate the HZ limits that may be used to evaluate the astrobiological potential of terrestrial exoplanets that will hopefully be discovered in the near future. Planets Gl 581c and 'd' are near, but outside, what can be considered as the conservative HZ. Planet 'c' receives 30% more energy from its star than Venus from the Sun, with an increased radiative forcing caused by the spectral energy distribution of Gl 581. Its habitability cannot however be positively ruled out by theoretical models due to uncertainties affecting cloud properties. Irradiation conditions of planet 'd' are comparable with those of early Mars. Thanks to the warming effect of CO2-ice clouds planet 'd' might be a better candidate for the first exoplanet known to be potentially habitable. A mixture of various greenhouse gases could also maintain habitable conditions on this planet.Comment: Astronomy and Astrophysics (2007) accepted for publicatio

Large isotope effect on TcT_c in cuprates despite of a small electron-phonon coupling

We calculate the isotope coefficients $\alpha$ and $\alpha^\ast$ for the superconducting critical temperature $T_c$ and the pseudogap temperature $T^\ast$ in a mean-field treatment of the t-J model including phonons. The pseudogap phase is identified with the $d$-charge-density wave ($d$-CDW) phase in this model. Using the small electron-phonon coupling constant $\lambda_d \sim 0.02$ obtained previously in LDA calculations in YBa$_2$Cu$_3$O$_7$, $\alpha^{\ast}$ is negative but negligible small whereas $\alpha$ increases from about 0.03 at optimal doping to values around 1 at small dopings in agreement with the general trend observed in many cuprates. Using a simple phase fluctuation model where the $d$-CDW has only short-range correlations it is shown that the large increase of $\alpha$ at low dopings is rather universal and does not depend on the existence of sharp peaks in the density of states in the pseudogap state or on specific values of the phonon cutoff. It rather is caused by the large depletion of spectral weight at low frequencies by the $d$-CDW and thus should also occur in other realizations of the pseudogap.Comment: 8 pages, 5 figures, to be publ. in PR