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, 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=${\mathit{k}}_{\mathit{F}}$+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 ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ and ${\mathrm{Bi}}_2$ ${\mathrm{Sr}}_2$ ${\mathrm{CaCu}}_2$ ${\mathrm{O}}_8$ systems is discussed.