Nonlinear optical study of surface electrons on Ba(Fe$_{1-x}$Co$_{x}$)$_2$As$_2$

We report second harmonic generation (SHG) measurements on single crystals of Ba(Fe$_{1-x}$Co$_{x}$)$_2$As$_2$. SHG from Ba(Fe$_{1-x}$Co$_{x}$)$_2$As$_2$ is dominated by surface contributions due to the broken inversion symmetry at the surface. By varying the polarization of incident ultrafast laser pulses, we demonstrate that SHG reveals the tetragonal crystal structure of Ba(Fe$_{1-x}$Co$_{x}$)$_2$As$_2$ at ambient conditions. We will discuss prospects of using SHG as a probe of the surface electrons, the in-plane anisotropy, and the dichotomy between surface and bulk superconductivity in iron-based superconductors.