Search for a nematic symmetry in the intra-unit-cell pseudogap states of underdoped Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta }$

We measure the intra-unit-cell pseudogap states (Y. Kohsaka \textit{et al}. \textit{Science} \textbf{315}, 1380 (2007)) in underdoped Bi$_{2}$Sr$_{2}$Ca$_{0.8}$Dy$_{0.2}$Cu$_{2}$O$_{8+\delta }$ ($T_{c}$=50K) using the Spectroscopic Imaging STM, and analyze this state using a local nematic order parameter. We search for the rotational symmetry breaking (nematicity) within each CuO$_{2}$~unit-cell in~ subatomic scale STM data with a particular care in correcting for instrumental drift. We investigate the correlation between this electronic nematicity and pseudogap energy scale.We discuss the relationship between the intra-unit-cell electronic structure and a nematicity.