Fermi arcs vs hole pockets: periodization of a cellular two-band model

TL;DR

This paper investigates whether Fermi arcs or hole pockets better describe the low-doping Fermi surface of cuprates, showing that current c-DMFT methods cannot definitively distinguish between them due to limitations in periodization.

Contribution

The authors introduce a simple self-energy parametrization demonstrating that c-DMFT periodization cannot conclusively differentiate Fermi arcs from hole pockets, highlighting the need for improved methods.

Findings

c-DMFT cannot definitively distinguish Fermi arcs from hole pockets

A simple parametrization reproduces c-DMFT spectral features

Proposes a new tiling scheme to recover hole and electron pockets

Abstract

It is still debated whether the low-doping Fermi surface of cuprates is composed of hole pockets or of disconnected Fermi arcs. Results from cellular dynamical mean field theory (c-DMFT) support the Fermi arcs hypothesis by predicting corresponding Fermi arcs for the Hubbard model. Here, we introduce a simple parametrization of the self-energy, in the spirit of Yang-Rice-Zhang theory, and show that state of the art c-CDMFT calculations cannot give a definitive answer to the question of Fermi arcs vs holes pockets, and this, independently of the periodization (cumulant or Green's function) used to display spectral weights of the infinite lattice. Indeed, when our model is restricted to a cluster and periodized like in c-DMFT, only two adjustable parameters suffice to reproduce the qualitative details of the frequency and momentum dependence of the low energy c-DMFT spectral weight for both periodizations. In other words, even though our starting model has a Fermi surface composed of hole and electron pockets, it leads to Fermi arcs when restricted to a cluster and periodized like in c-DMFT. 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.