Phonon-driven superconductivity in the vicinity of ferroelectric and charge density wave ordering in La(O,F)BiX$_2$ (X=S, Se, O)

Examples of layered superconductors include cuprates, MgB$_2$, CaC$_6$, and recent iron-pnictides. Recently a new family of layered materials containing BiS$_2$ planes, was discovered to be superconducting at temperatures up to 10 K. In order to reveal the mechanism of superconductivity, here we present results from first-principles calculations with many surprising findings for La(O,F) Bi X$_2$ for X=S, Se, and O. The parent compound LaOBiS$_2$ possesses anharmonic ferroelectric soft phonons at the zone center with a rather large polarization of P $\approx$ 10 $\mu$C/cm$^2$. Upon electron doping, new unstable phonon branches appear along the entire line Q=(q,q,0), causing Bi/S atoms to order in a one-dimensional charge density wave (CDW). We find that BiS$_2$ is a strong electron-phonon coupled superconductor in the vicinity of competing ferroelectric and CDW phases. We discuss similar results for X=Se and hypothetical compound X=0. These results will be compared with another interesting system, namely Ba$_{1-x}$K$_x$BiO$_3$, which exhibits several phases, including CDW, an incommensurate pseudo ferroelectric, and superconductivity at 31 K. Our results suggest new directions to tune the balance between these phases and increase T$_c$ in this new class of materials.