Electronic structure properties and superconductivity of the $\beta$-pyrochlore Os oxides, $A$Os$_2$O$_6$ ($A$=alkali metal)

The recently discovered\footnote{T. Muramatsu {\it et al.} J. Phys. Soc. Jpn. {\bf 73}, 10 (2004).} family of superconducting $\beta$-pyrochlores {\it A}Os$_2$O$_6$ ($A$=alkali metal) represents a particularly interesting example of the interplay between superconductivity and orbital and crystal structure degrees of freedom. Indeed, the pyrochlore lattice formed by the Os-O staggered chains appears to lead to very high Sommerfeld coefficients, increasing of $T_c$ under positive pressure, and other intriguing properties. We present results of a first-principles study of the electronic structure and superconducting properties of these materials ($A$=Na, K, Rb, and Cs) using the highly precise full-potential linearized augmented plane wave (FLAPW) method.\footnote{Wimmer, Krakauer, Weinert, Freeman, Phys. Rev. B {\bf 24}, 864 (1981).} We show that the observed increase of $T_c$ with decreasing mass of $A$ as well as under positive hydrostatic pressure can both be well understood within a conventional phonon-mediated pairing picture. Furthermore, the density of states at $E_F$ depends critically on spin-orbit coupling, due to a van Hove singularity near $E_F$, with a direct effect on $T_c$; the Fermi surface shows strong nesting, which is reflected in the dynamic susceptibility and thus indicates that spin fluctuations may play an important role in these materials.