Nature of local distortions in newly-discovered disordered superconductor, LaO$_{\mathrm{1-x}}$F$_{\mathrm{x}}$BiS$_{2}$

LaO$_{\mathrm{1-x}}$F$_{\mathrm{x}}$BiS$_{2}$ is a disordered, non-magnetic superconductor belonging to the novel family of BiS$_{2}$ layered superconductors. The parent phase, LaOBiS$_{2}$, is a band insulator with tetragonal structure (P4/nmm space group). The highest T$_{\mathrm{c}}$ of LaO$_{\mathrm{1-x}}$F$_{\mathrm{x}}$BiS$_{2}$ is attained at x $=$ 0.5, as 10.8 K. Upon F doping or temperature change, little change had been reported in the low-energy portion of the phonon spectrum and the question whether LaO$_{0.5}$F$_{0.5}$BiS$_{2}$ is a BCS superconductor or not remains unsolved. The local atomic structures of LaOBiS$_{2}$ and LaO$_{0.5}$F$_{0.5}$BiS$_{2}$ were investigated as a function of temperature by using elastic neutron scattering and the pair density function analysis from 6 to 300 K and 2 to 300K respectively. We present possible models of local structure of LaOBiS$_{2}$ and LaO$_{0.5}$F$_{0.5}$BiS$_{2}$ which qualitatively explain the temperature dependence and composition dependence.