Intra unit cell electronic structure of the d-symmetry form factor density wave in the underdoped cuprates -- Part I

A central issue of cuprate superconductivity research is to understand the nature of the unknown phase called the \textit{pseudogap} and its relationship to the $d$-wave superconductivity. To approach this we use spectroscopic imaging STM to study the electronic structure of Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta}$. Using our recently developed technique of sub-lattice phase-resolved electronic structure visualization within each CuO$_{2}$ unit-cell, we discovered a $d$-symmetry form factor density wave within the cuprate pseudogap state. In this talk, part I, we demonstrate that $d$-symmetry is the predominant form factor in the density wave within pseudogap states and show how this situation evolves upon doping.