Quasiparticle spectrum in a nearly antiferromagnetic Fermi liquid: Shadow and flat bands.

Abstract

We consider a two-dimensional Fermi liquid in the vicinity of a spin-density-wave transition to a phase with commensurate antiferromagnetic long-range order. We assume that near the transition, the Fermi surface is large and crosses the magnetic Brillouin zone boundary. We show that under these conditions, the self-energy corrections to the dynamical spin susceptibility, \ensuremath{\chi}(q,\ensuremath{\omega}), and to the quasiparticle spectral function, A(k,\ensuremath{\omega}), are divergent near the transition. We identify and sum the series of most singular diagrams, and obtain a solution for \ensuremath{\chi}(q,\ensuremath{\omega}) and an approximate solution for A(k,\ensuremath{\omega}). We show that (i) A(k) at a given, small \ensuremath{\omega} has an extra peak at k=${\mathit{k}}_{\mathit{F}}$+\ensuremath{\pi} (shadow band), and (ii) the dispersion near the crossing points is much flatter than for free electrons. The relevance of these results to recent photoemission experiments in ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ and ${\mathrm{Bi}}_{2}$${\mathrm{Sr}}_{2}$${\mathrm{CaCu}}_{2}$${\mathrm{O}}_{8}$ systems is discussed.