van Hove Singularity effects in Strongly Correlated Fermions

Abstract

We examine the effects of a van Hove singularity (vHs) in the density of states (DOS) of a two dimensional, $t-t'-U$ Hubbard model within the local approximation. Within our approximation the non-interacting Fermi surface is always retained away from half-filling; and we find that the vHs in the DOS survives, and for hole doping is nearly "pinned" to the Fermi level due to the enhancement of the effective mass, $m^*$. We discuss the electron-hole asymmetry of this phenomena and its relevance to the electron and hole doped cuprates. At optimal (hole) doping, with the Fermi level at the vHs, we find that the single particle damping rate $Γ$, and the resistivity $ρ_{dc}$, scale as $T$ for moderately low temperatures ($T \gtrsim 100$K), while for the electron doped system $Γ$ and $ρ_{dc} \sim T^2$.