Fermi surface evolution in underdoped cuprates

Abstract

We consider a two-dimensional Fermi liquid coupled to low-energy commensurate spin fluctuations. At small coupling, the hole Fermi surface is large and centered around $(π,π)$. We show that as the coupling increases, the shape of the Fermi surface undergoes a substantial evolution, and at strong coupling, the hole Fermi surface consists of small pockets centered at $(\pm π/2, \pm π/2)$. At intermediate couplings, there exists a large hole Fermi surface centered at $(π,π)$ as well as four hole pockets, but the quasiparticle residue is small everywhere except for the pieces of the pockets which face the $Γ$ point. The relevance of these results to recent photoemission experiments in $YBCO$ and $Bi2212$ systems, and their relation to the Luttinger theorem are discussed.