26 - Collective excitations in the ground state of a two-dimensional attractive Fermi gas

Summary

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/ε_F, where ε₀ is the two-fermion binding energy and ε_F 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/ε_F> 1) the spectrum is continuous and has the Bogolubov form, but in the weak-coupling limit (ε₀/ε_F«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 q_c≃ 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/ε_F≃¼.

Introduction

Since the discovery of high-T_c 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- T_c superconductors, most of which have a layered structure, have a short coherence length, so that k_Fξ₀≃1, where k_F is the Fermi momentum.