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Abstract

A metallic electron system near an orientational symmetry breaking
Pomeranchuk instability is characterized by a "soft" Fermi surface with
enhanced collective fluctuations. We analyze fluctuation effects in a
two-dimensional electron system on a square lattice in the vicinity of
a Pomeranchuk instability with d-wave symmetry, using a
phenomenological model which includes interactions with a small
momentum transfer only. We compute the dynamical density correlations
with a d-wave form factor for small momenta and frequencies, the
dynamical effective interaction due to a fluctuation exchange, and the
electron self-energy. At the quantum critical point the density
correlations and the dynamical forward scattering interaction diverge
with a dynamical exponent z=3. The singular forward scattering leads to
large self-energy corrections, which destroy Fermi liquid behavior over
the whole Fermi surface except near the Brillouin zone diagonal. The
decay rate of single-particle excitations, which is related to the
width of the peaks in the spectral function, exceeds the excitation
energy in the low-energy limit. The dispersion of maxima in the spectra
flattens strongly near those portions of the Fermi surface which are
remote from the zone diagonal. The contribution from classical
fluctuations to the self-energy spoils (omega/T) scaling in the quantum
critical regime.