Fermi Arcs in the Superconducting Clustered State for Underdoped Cuprates

The one-particle spectral function of a state formed by superconducting (SC) clusters is studied via Monte Carlo techniques. The clusters have similar SC amplitudes but randomly distributed phases. This state is stabilized by the competition with anti-ferromagnetism, after quenched disorder is introduced. Fermi arcs between the critical temperature Tc and the cluster formation temperature scale T* are observed, similarly as in the pseudo-gap state of the cuprates. The arcs originate at metallic regions in between the neighboring clusters that present large SC phase differences.