Coincidence of checkerboard charge order and antinodal state decoherence in strongly underdoped superconducting Bi2Sr2CaCu2O8+δ

The doping dependence of nanoscale electronic structure in superconducting Bi2Sr2CaCu2O8+delta is studied by scanning tunneling microscopy. At all dopings, the low energy density-of-states modulations are analyzed according to a simple model of quasiparticle interference and found to be consistent with Fermi-arc superconductivity. The superconducting coherence peaks, ubiquitous in near-optimal tunneling spectra, are destroyed with strong underdoping and a new spectral type appears. Exclusively in regions exhibiting this new spectrum, we find local "checkerboard" charge ordering of high energy states, with a wave vector of (Q) over right arrow=(+/- 2 pi/4.5a(0),0); (0,+/- 2 pi/4.5a(0))+/- 15%. Surprisingly, this spatial ordering of high energy states coexists harmoniously with the low energy Bogoliubov quasiparticle states.