Non-Fermi Liquid Fixed Point in 2+1 Dimensions

We construct models of excitations about a Fermi surface that display calculable deviations from Fermi liquid behavior in the low-energy limit. They arise as a consequence of coupling to a Chern-Simons gauge field, whose fluctations are controlled through a 1 kx interaction. The Fermi liquid fixed point is shown to be unstable in the infrared for x < 1, and an infrared-stable fixed point is found in a (1 − x)-expansion, analogous to the ǫ-expansion of critical phenomena. x = 1 corresponds to Coulomb interactions, and in this case we find a logarithmic approach to zero coupling. We describe the low-energy behavior of metals in the universality class of the new fixed point, and discuss its possible application to the compressible ν = 1 2 quantum Hall state and to the normal state of copper-oxide superconductors.