The electron gas with short coherence length pairs: how to approach the stronger coupling limit? M. Letz * Institutf  urPhysik,JohannesGutenbergUniversit at,StaudingerWeg7,D-55099Mainz,Germany Received 4 September 2000; received in revised form 9 November 2000; accepted 10 November 2000 Abstract The attractive Hubbard model is investigated in 2D using a T -matrix approach. In a self-consistent calculation pairs as in®nite lifetime Bosons only exist in the atomic limit and therefore a Fermi surface can be investigated also in the stronger coupling regime. A heavy quasiparticle peak with a weak dispersion crosses the Fermi surface at k F whereas light, single particle excitations do only exist far away from the Fermi surface. At low temperatures there seem to exist dierent self-consistent solutions. In one of them a pseudogap opens even in the integrated density of states. In the present work accurate k-dependent and k-integrated spectral quantities for a 2D ®nite lattice are presented. Ó 2001 Elsevier Science B.V. All rights reserved. PACS: 74.20 Mn; 74.25.-q; 74.25.Fy; 74.25.Nf; 74.72.-h; 74.20-z Keywords: Attractive Hubbard model; Two-particle bound states; Pseudo-gap; Non-Fermi-liquid properties 1. Introduction One of the main enigmae which has to be solved for the high-T c cuprates and other unusual super- conductors like the heavy Fermion compounds is connected with the short coherence length of the Cooper pairs. This short coherence length was the foundation for a scenario where tightly bound pairs are formed already above T c . The simplest thinkable model system which is suited to investi- gate the parameter region of stronger coupling is the attractive Hubbard model. The Hubbard model with a simple on site attraction fails to de- scribe superconductivity with a non-spherical gap parameter. We believe however that the problem of short range superconductivity with a strong electron±electron or hole±hole, in the following part of the paper the word electrons can be re- placed by the word holes discussing in this way hole-superconductivity) attraction has to be un- derstood ®rst before the question of a non-s-wave order parameter can be addressed properly. The electron gas with an attractive interaction has be- sides the atomic limit two well understood border line cases. One is the 3D weak coupling limit where the attractive interaction between the charge car- riers is so weak that no two-particle bound state will be formed below the one particle continuum. Since no two-particle bound state can be formed below the one-particle continuum the Fermi sur- face remains intact when lowering the temperature Physica C 353 2001) 71±76 www.elsevier.nl/locate/physc * Tel.: +49-6131-394214; fax: +49-6131-395441. E-mail address: letz@haldane.physik.uni-mainz.de M. Letz). 0921-4534/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII:S0921-453400)01742-1