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Near doping-independent pocket area from an antinodal Fermi surface instability in underdoped high temperature superconductors

Fermi surface models applied to the underdoped cuprates predict the small pocket area to be strongly dependent on doping whereas quantum oscillations in YBa2Cu3O6+x find precisely the opposite to be true; seemingly at odds with the Luttinger volume. We show that such behavior can be explained by an incommensurate antinodal Fermi surface nesting-type instability; further explaining the doping-dependent superstructures seen in cuprates using scanning tunneling microscopy. We develop a Fermi surface reconstruction scheme involving orthogonal density waves in two-dimensions and show that their incommensurate behavior requires momentum-dependent coupling. A co-operative modulation of the charge and bond-strength is therefore suggested.