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

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, 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=kF+{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 YBa₂{Cu}₃O_7-δ and Bi₂{Sr}₂CaCu₂{O}₈$ systems is discussed.