Density functional theory of superconductivity in doped tungsten oxides

We apply density functional theory for superconductors (SCDFT) to doped tungsten oxide in three forms: electrostatically doped WO3, perovskite WO3−xFx, and hexagonal CsxWO3. We achieve a consistent picture in which the experimental superconducting transition temperature Tc is reproduced, and superconductivity is understood as a weak-coupling state sustained by soft vibrational modes of the WO6 octahedra. SCDFT simulations of CsxWO3 allow us to explain the anomalous Tc behavior observed in most tungsten bronzes, where Tc decreases with increasing carrier density. Here, the opening of structural channels to host Cs atoms induces a softening of strongly coupled W-O modes. By increasing the Cs content, these modes are screened and Tc is strongly reduced

Direct evaluation of the isotope effect within the framework of density functional theory for superconductors

Within recent developments of density functional theory, its numerical implementation and of the superconducting density functional theory is nowadays possible to predict the superconducting critical temperature, Tc, with sufficient accuracy to anticipate the experimental verification. In this paper we present an analytical derivation of the isotope coefficient within the superconducting density functional theory. We calculate the partial derivative of Tc with respect to atomic masses. We verified the final expression by means of numerical calculations of isotope coefficient in monatomic superconductors (Pb) as well as polyatomic superconductors (CaC6). The results confirm the validity of the analytical derivation with respect to the finite difference methods, with considerable improvement in terms of computational time and calculation accuracy. Once the critical temperature is calculated (at the reference mass(es)), various isotope exponents can be simply obtained in the same run. In addition, we provide the expression of interesting quantities like partial derivatives of the deformation potential, phonon frequencies and eigenvectors with respect to atomic masses, which can be useful for other derivations and applications