Fermi surface fluctuations and breakdown of Fermi liquid behavior

Electron-electron interactions can induce Fermi surface deformations which break the point-group symmetry of the crystal structure of the system. In the vicinity of such a "Pomeranchuk instability" the Fermi surface is easily deformed by anisotropic perturbations, and exhibits enhanced collective fluctuations. We analyze Fermi surface fluctuation effects in a two-dimensional electron system on a square lattice in the vicinity of a Pomeranchuk instability with d-wave symmetry. At a quantum critical point d-wave 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 contribution from classical fluctuations to the self-energy spoils omega/T scaling in the quantum critical regime. We discuss to what extent d-wave Fermi surface fluctuations may play a role in cuprate superconductors.