Origin of the Extended Van Hove region in Cuprate Superconductors

Abstract

We study the evolution of the quasiparticle dispersion with doping for the two-dimensional $t\ensuremath{-}{t}^{\ensuremath{'}}\ensuremath{-}{t}^{\ensuremath{'}\ensuremath{'}}\ensuremath{-}J$ model using the exact diagonalization technique and present a consistent theoretical analysis. Both calculations show that the flat region around $(\ensuremath{\pi},0)$ does not exist at half filling, however, it appears in the underdoped regime and remains almost unchanged upon additional doping. The enhancement of the incoherent motion of holes induced especially by the ${t}^{\ensuremath{'}}$ and ${t}^{\ensuremath{'}\ensuremath{'}}$ terms accounts for the formation of the extended Van Hove region. Our results are in excellent agreement with the recent photoemission experiments on ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{Ca}}_{1\ensuremath{-}x}{\mathrm{Dy}}_{x}{\mathrm{Cu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ [Marshall et al., Phys. Rev. Lett. 76, 4841 (1996)].