Can Short-Range CDW Order Cause the Fermi Surface Reconstruction in the Cuprates?

In the cuprates, short-range charge density wave (CDW) order is generally thought to account for the reconstructed Fermi surface apparent in quantum oscillation (QO) experiments. However, since the measured CDW correlation length may sometimes be shorter than the cyclotron radius, it is unclear whether sharp QOs reflecting the reconstructed Fermi surface are theoretically expected. In this work, we derive a simple quantization rule appropriate for disordered CDWs and show that it involves a random Berry phase. We demonstrate that under most circumstances, the predicted QO amplitude is not easily reconciled with observations in the cuprates.