Cuprate quantum phase transition probed by nanoscale density wave inhomogeneity*

The cuprate phase diagram exhibits a number of ordered phases in addition to superconductivity, and it has long been postulated that a quantum critical point - separating the notoriously unconventional underdoped regime from the overdoped so-called Fermi liquid - may influence a large region of the phase diagram. Experiments to uncover the electronic correlations giving rise to the complex phenomenology are key to understanding the complete ground state evolution.

Here, we use the d-form factor density wave (DW), imaged via scanning tunneling microscopy, to probe the ground state evolution in superconducting (Pb,Bi)₂(Sr,La)₂CuO_6+δ (Bi-2201). We employ the disorder caused by local dopant inhomogeneity to gain continuous access to the doping axis of the phase diagram, both via standard Fourier techniques and machine learning. We find a transition in the DW from commensurate to incommensurate, which occurs simultaneously with the Fermi surface transition, where open arcs are replaced by a conventional large Fermi surface. The coincidence of these transitions indicates an intimate link between the commensurate instability and the mechanism underlying the Fermi arcs.