Deviations from Fermi-Liquid behaviour in (2+1)-dimensional Quantum Electrodynamics and the normal phase of high-$T_c$ Superconductors

Abstract

We argue that the gauge-fermion interaction in multiflavour quantum electrodynamics in $(2 + 1)$-dimensions is responsible for non-fermi liquid behaviour in the infrared, in the sense of leading to the existence of a non-trivial (quasi) fixed point that lies between the trivial fixed point (at infinite momenta) and the region where dynamical symmetry breaking and mass generation occurs. This quasi-fixed point structure implies slowly varying, rather than fixed, couplings in the intermediate regime of momenta, a situation which resembles that of (four-dimensional) `walking technicolour' models of particle physics. The inclusion of wave-function renormalization yields marginal $O(1/N)$-corrections to the `bulk' non-fermi liquid behaviour caused by the gauge interaction in the limit of infinite flavour number. Such corrections lead to the appearance of modified critical exponents. In particular, at low temperatures there appear to be logarithmic scaling violations of the linear resistivity of the system of order $O(1/N)$. Connection with the anomalous normal-state properties of certain condensed matter systems relevant for high-temperature superconductivity is briefly discussed. The relevance of the large (flavour) $N$ expansion to the fermi-liquid problem is emphasized. As a partial result of our analysis, we point out the absence of Charge-Density-Wave Instabilities from the effective low-energy theory, as a consequence of gauge invariance.