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We observe apparent hole pockets in the Fermi surfaces of single-layerBi-based cuprate superconductors from angle-resolved photoemission (ARPES).From detailed low-energy electron diffraction measurements and an analysis ofthe ARPES polarization-dependence, we show that these pockets are notintrinsic, but arise from multiple overlapping superstructure replicas of themain and shadow bands. We further demonstrate that the hole pockets reportedrecently from ARPES [Meng et al, Nature 462, 335 (2009)] have a similarstructural origin, and are inconsistent with an intrinsic hole pocketassociated with the electronic structure of a doped CuO$_2$ plane. The natureof the Fermi surface topology in the enigmatic pseudogap phase thereforeremains an open question.

Structural origin of apparent Fermi surface pockets in angle-resolved photoemission of Bi$_2$Sr$_{2-x}$La$_x$CuO$_{6+\delta}$