Abstract

The spectrum of collective (pair) excitations in the ground state of a dilute twodimensional (2D) attractive Fermi-gas is studied within the functional integral formalism. The linearized equations for the fluctuations about the non-trivial saddle point are analyzed for all coupling regimes, which are characterized by the ratio ε0/εF, where ε0 is the two-fermion binding energy and εF is the Fermi energy. The approximation takes into account propagation of the fluctuations and their interaction with the condensate. In the strong-coupling, or ‘;Bosegas’, regime (ε0/εF> 1) the spectrum is continuous and has the Bogolubov form, but in the weak-coupling limit (ε0/εF«1) there are two types of excitations (different from the two-fermion scattering states): (i) long-wavelength sound-like excitations with the cut-off at momentum qc≃ l/ξ0 (where ξ0 is the Cooper pair size), and (ii) pair excitations with q≃ (8mμ)½, where μ is the chemical potential and m is the fermion mass. The crossover between weakand strong-coupling behavior of the excitation spectrum is found to occur at the value of the coupling parameter ε0/εF≃¼.

Introduction

Since the discovery of high-Tc superconductivity there has been growing interest in studying 2D Fermi gases with attractive interaction, especially in the crossover regime, when the pair size ξ0 is of the order of the interparticle distance. The importance of such a model, which can be regarded as a semiphenomenological model of a 2D superconductor, is highlighted by experimental evidence that the high- Tc superconductors, most of which have a layered structure, have a short coherence length, so that kFξ0≃1, where kF is the Fermi momentum.