Fermi arcs vs hole pockets

Many phenomena in cuprates can be explained using cluster extensions of dynamical mean-field theory [1]. This methodology resolves the dichtomy between local and non-local plysics through a self-consistency condition. It provides a unified picture of many phenomena in cuprates, in particular those associated with the pseudogap [2][3]. However, predicting details of the Fermi surface requires an additional step known as periodization. Here [4] we show that the observation of Fermi arcs is not sufficient to definitely conclude whether there are Fermi arcs. To show this, we introduce a simple parametrization of the self-energy (c-2B), in the spirit of Yang-Rice-Zhang theory, and show that Fermi arcs can appear when hole pockets should be the correct answer, and this, independently of the periodization (cumulant or Green's function) used to display spectral weights of the infinite lattice. In addition, only two adjustable parameters in this simple c-2B model suffice to reproduce the qualitative details of the frequency and momentum dependence of the low energy Cellular Dynamical Mean-Field Theory (c-DMFT) spectral weight for both periodizations. We provide a new "compact tiling" scheme to recover the hole and electron pockets of our starting non-interacting lattice model, suggesting that better periodization schemes might exist.