STM Studies of the Lattice Distortion at the Surface of Ba(Fe$_{1-x}$Co$_{x})_{2}$As$_{2}$

At low temperatures the bulk of the iron pnictides such as Ba(Fe$_{1-x}$Co$_{x})_{2}$As$_{2}$ goes from an orthorhombic structure phase to the tetragonal phase with doping. This phase transition is also accompanied by a magnetic phase transition. These phenomena have been discussed in the context of the mechanism of superconductivity in the iron pnictides. With careful examination of our low temperature STM topographic images on the single crystals of Ba(Fe$_{1-x}$Co$_{x})_{2}$As$_{2}$, we found that$_{ }$the lattice distortions of the two observed surface structures, namely ``Root 2'' and ``1$\times $2'', evolve with doping concentration x across the superconducting dome. Starting from parent compound, the orthorhombic ``Root 2'' structure evolves towards rhombic, while the ``1$\times $2'' structure evolves from rhombic to orthorhombic. We will discuss the implications of such doping dependent lattice distortion.