The local structure of self-doped BiS$_2$-based layered systems as a function of temperature

We have studied the local structure of layered Eu(La,Ce)FBiS$_{2}$ compounds by Bi L$_3$ - edge extended x-ray absorption fine structure (EXAFS) measurements as a function of temperature. We find that BiS$_2$ sub-lattice is largely distorted in EuFBiS$_{2}$, characterized by two different in-plane Bi-S1 distances. The distortion is marginally affected by partial substitutions of Ce (Eu$_{0.5}$Ce$_{0.5}$FBiS$_2$) and La (Eu$_{0.5}$La$_{0.5}$FBiS$_2$). Temperature dependent local structure distortion reveals an indication of possible charge density wave like instability in the pristine self-doped EuFBiS$_{2}$ and Ce substituted Eu$_{0.5}$Ce$_{0.5}$FBiS$_2$ while it is suppressed in La substituted Eu$_{0.5}$La$_{0.5}$FBiS$_2$. In the compounds with higher superconducting transition temperature, the axial Bi-S2 bond distance is elongated and the related bond stiffness decreased, suggesting some important role of this in the charge transfer mechanism for the self-doping in the active BiS$_2$-layer. In-plane Bi-S1 distances are generally softer than axial Bi-S2 and they suffer further softening by the substitutions. The results are discussed in relation to an important role of the Bi defect chemistry driven asymmetric local environment in the physical properties of these materials.