Journal of Low Temperature Physics, VoL 99, Nos. 3/4, I995 Non Fermi liquid behavior in semimetals. Applications to the fullerenes. F. Guinea, J. Gonz~ilez* and M. A. H. Vozmediano t Instituto de Ciencia de Materiales. Consejo Superior de Investigaciones Cientificas. Cantoblanco. ~80.i9 Madrid. Spain. * Instituto de Es~ructura de Ia Materia. Consejo Superior de Investigaciones Cient{ficas. Serrano 123, 28006 Madrid. Spain. t Eseuela Politgcniea Superior. Universidad Carlos III. Butarque 15. Legends. 28913 Madrid. Spain. In a variety of semimetaIs with vanishing density of s~ates a the Fermi level, the low energy electronic states are described by an effective Dirac equation, instead of the more conventional effective mass appromimation (equivalent to SchrJdinger equation}. When this happens, electron-electron ir~teractions give vise ~o anomalous features, which differ from those of conventional metals and insulators. A compre- hensive discussion of these effects is presented, making use of the fact that Dirac electrons ir~teracting through Coulomb forces lead to a well defined, renormalizable, quantum field theory, which has many similarities to quantum electrodynamics. The most remarkable feature is the absence of a coherent quasipartiele pole, like in 1D Luttinger liquids. PACS numbers: 05.30 Jp, 71.~8.§ 75.10 Lp I. INTRODUCTION A variety of materials in two and three dimensions show a vanishing density of states at the Fermi level, being in the threshold between metals (with a finite density of states) and insulators (where a true gap exists). Commonly, this effect is due to band crossings at special points in the Brillouin Zone, imposed by symmetry considerations. The simplest example is given by a family of lattices with two equivalent sites per unit cell, of which the honeycomb and the diamond structure are particular examples. 1 A tight binding model with one orbital per site in such a lattice exhibits the vanishing density of states mentioned above. In the present work, we will concentrate ourselves on the study of the 2D honeycomb lattice, as a model relevant to the fullerene compounds, which can be considered as curved structures made up from this lattice. ~ Most considerations, however, apply to a much wider variety of systems. The vanishing of the density of states at the Fermi level implies that a screening 287 0022-2291/95/0500-0287507,50/0 9 1995 Plenum Publishing Corporation