Physics – Condensed Matter
Scientific paper
1995-04-04
Physics
Condensed Matter
a sign and amplitude of the vertex renormalization and few typos are corrected
Scientific paper
10.1103/PhysRevB.52.R3840
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.
Chubukov Andrey V.
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