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Electron-Phonon Superconductivity in LaO$_{0.5}$F$_{0.5}$BiSe$_{2}$

We report density functional calculations of the electronic structure, Fermi surface, phonon spectrum and electron--phonon coupling for newly discovered superconductor LaO$_{0.5}$F$_{0.5}$BiSe$_{2}$. Significant similarity between LaO$_{0.5}$F$_{0.5}$BiS$_{2}$ and LaO$_{0.5}$F$_{0.5}$BiSe$_{2}$ is found, i.e. there is a strong Fermi surface nesting at ($π$,$π$,0), which results in unstable phonon branches. Combining the frozen phonon total energy calculations and an anharmonic oscillator model, we find that the quantum fluctuation prevents the appearance of static long--range order. The calculation shows that LaO$_{0.5}$F$_{0.5}$BiSe$_{2}$ is highly anisotropic, and same as LaO$_{0.5}$F$_{0.5}$BiS$_{2}$, this compound is also a conventional electron-phonon coupling induced superconductor.