Chuck-Hou Yee Minor edits  over 7 years ago

Commit id: 5bf4e22485f6383f7ffbbddca1a0f9df03513131

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Potassium-doped barium bismuth oxide ($Ba_{1-x} K_x Bi O_3$), is a famous high temperature superconductor, discovered in the late 1980s~\cite{Sleight_1975, Cava_1988}. Its parent compound, BaBiO$_3$, has a distorted perovskite structure, with a band gap of $\sim 0.2$~eV~\cite{Sleight_1975}. Doping the material, with K for example, suppresses the structural distortions and makes the material superconducting, with a transition temperature of nearly 30~K at optimal doping. DFT does not describe the insulating character of the parent compound. Additionally, DFT estimates of the electron phonon coupling $\lambda$ within Migdal-Eliasberg theory give a value of 0.34 in the doped compound, too small to account for its superconductivity~\cite{Meregalli_1998}.  Examining We examined  the effect of correlations, we correlations and  found that $\lambda$ is substantially enhanced relative to its DFT estimate toa value of  nearly $1.0$, and that this enhancement is responsible for superconductivity in doped BaBiO$_3$~\cite{Yin_2013}. We argue argued  that correlations similarly enhance the electron phonon coupling in other materials proximate to an insulating state, accounting for superconductivity in systems such as HfNCl, borocarbides and buckminsterfullerenes. For these materials the most important type of correlation that needs to be treated is the static (in the solid state physicist convention) correlations. Hence a GW, or a hybrid DFT calculation is enough to correct the electronic structure of this material. After these calculations are done, one is left with a strongly coupled electron phonon system (after the static corrections to the Kohn Sham potential $\lambda ~ \sim  1$). This coupling induces a large dynamical self energy, which accounts for the anomalous optical properties of this system~\cite{Nourafkan_2012} at relatively low energies ( less than 1 ev). Following M. Norman's cited above, we searched for other materials in that class. Materials whose parent compound would be strongly mixed valent and where the electron phonon coupling would be understimated by LDA, so that they would be candidates to be another " other high temperature superconductor".