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

TL;DR

This paper analyzes the quasiparticle spectrum near a spin-density-wave transition in a 2D Fermi liquid, revealing shadow bands and flat dispersions that relate to experimental observations in high-temperature superconductors.

Contribution

It provides a theoretical framework for understanding shadow and flat bands in nearly antiferromagnetic Fermi liquids, including summing divergent diagrams and deriving spectral functions.

Findings

Identification of shadow bands at $k = k_F + ext{pi}$

Discovery of flatter dispersion near crossing points

Relevance to photoemission experiments in cuprates

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