Fermi surface fluctuations and single electron excitations near Pomeranchuk instability in two dimensions

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.