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, $χ(q, ω)$, and to the quasiparticle spectral function function, $A(k, ω)$, are divergent near the transition. We identify and sum the series of most singular diagrams, and obtain a solution for $χ(q, ω)$ and an approximate solution for $A(k, ω)$. We show that (i) $A(k)$ at a given, small $ω$ has an extra peak at $k = k_F + π$ (`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 $YBCO$ and $Bi2212$ systems is discussed.