  One of the main challenges in understanding high TC superconductivity is to
disentangle the rich variety of states of matter that may coexist, cooperate,
or compete with d-wave superconductivity. At center stage is the pseudogap
phase, which occupies a large portion of the cuprate phase diagram surrounding
the superconducting dome [1]. Using scanning tunneling microscopy, we find that
a static, non-dispersive, "checkerboard"-like electronic modulation exists in a
broad regime of the cuprate phase diagram and exhibits strong doping
dependence. The continuous increase of checkerboard periodicity with hole
density strongly suggests that the checkerboard originates from charge density
wave formation in the anti-nodal region of the cuprate Fermi surface. These
results reveal a coherent picture for static electronic orderings in the
cuprates and shed important new light on the nature of the pseudogap phase.
