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We bring resolution to the longstanding problem relating Fermi surfacereconstruction to the number of holes contained within the Fermi surface volumein underdoped high Tc superconductors. On considering uniaxial and biaxialcharge-density wave order, we show that there exists a relationship between theordering wave vector, the hole doping and the cross-sectional area of thereconstructed Fermi surface whose precise form depends on the volume of thestarting Fermi surface. We consider a `large' starting Fermi surface comprising1+p hole carriers, as predicted by band structure calculations, and a `small'starting Fermi surface comprising p hole carriers, as proposed in models inwhich the Coulomb repulsion remains the dominant energy. Using thereconstructed Fermi surface cross-sectional area obtained in quantumoscillation experiments in YBa2Cu3O6+x and HgBa2CuO4+x and the establishedmethods for estimating the chemical hole doping, we find the ordering vectorsobtained from x-ray scattering measurements to show a close correspondence withthose expected for the small starting Fermi surface. We therefore show theCoulomb repulsion to remain largely unscreened throughout the entire underdopedregime where the pseudogap exists and further show that the quantum oscillationfrequency and charge-density wave vectors provide accurate estimates for thenumber of holes contributing to the Fermi surface volume.

The number of holes contained within the Fermi surface volume in underdoped high temperature superconductors