Density wave as a probe of the full cuprate phase diagram*

In cuprate materials, the strong correlations in proximity to the antiferromagnetic Mott insulating state give rise to an array of unconventional phenomena beyond high temperature superconductivity. Developing a complete description of the ground state evolution is crucial to decoding the complex phase diagram. Here we use the structure of broken translational symmetry, namely d-form factor charge modulations in (Bi,Pb)₂(Sr,La)₂CuO_6+δ, as a probe of the ground state reorganization which occurs at the transition from truncated Fermi arcs to a large Fermi surface. We use real space imaging of local electronic inhomogeneity as a tool to access a range of dopings within each sample, and we firmly establish the spectral gap Δ as a proxy for local hole doping. From the Δ-dependence of the charge modulation wavevector, we discover a commensurate to incommensurate transition that is coincident with the Fermi surface transition from arcs to large hole pocket, demonstrating the qualitatively distinct nature of the electronic correlations governing the two sides of this quantum phase transition. Furthermore, the doping dependence of the incommensurate wavevector on the overdoped side is at odds with a simple Fermi surface driven instability.