Pair fluctuations in the ground state of a two-dimensional attractive Fermi gas

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Sergei V. Traven

Crossover of the pair excitation spectrum in the ground state of a dilute two-dimensional Fermi gas is studied as a function of the attraction strength $\frac{{\ensuremath{\varepsilon}}_{0}}{{\ensuremath{\varepsilon}}_{F}}$, where ${\ensuremath{\varepsilon}}_{0}$ is the two-fermion binding energy and ${\ensuremath{\varepsilon}}_{F}$ is the Fermi energy. It is shown that at $\frac{{\ensuremath{\varepsilon}}_{0}}{{\ensuremath{\varepsilon}}_{F}}\ensuremath{\simeq}\frac{1}{4}$ the spectrum changes its character from the continuous one in the strong-coupling, or "Bose-gas," limit ($\frac{{\ensuremath{\varepsilon}}_{0}}{{\ensuremath{\varepsilon}}_{F}}\ensuremath{\gg}1$) to that which consists of two different types of excitations in the weak-coupling ($\frac{{\ensuremath{\varepsilon}}_{0}}{{\ensuremath{\varepsilon}}_{F}}\ensuremath{\ll}1$) regime: (i) long-wavelength soundlike mode with the cutoff at momentum ${q}_{c}\ensuremath{\sim}\frac{1}{{\ensuremath{\xi}}_{0}}$, and (ii) pair excitations with $q\ensuremath{\ge}\sqrt{8m\ensuremath{\mu}}$.

Chengdong He, Entong Zhao, Zejian Ren +3 more

No author provided

The excitation spectrum of pair fluctuations in the ground state of a dilute two-dimensional (2D) attractive Fermi-gas is studied for different coupling regimes. In the strong-coupling limit the spectrum has the Bogolubov form, but in the weak-coupling regime there are two types of the pair excitations (different from two-fermion scattering states): (i) long-wavelength collective mode with the cutoff at momentum q(c) similar to 1/xi(0), where xi(0) is the pair size, and (ii) pair excitations with q greater than or equal to root 8m mu.

Sergei V. Traven

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 ε 0 /ε F , where ε 0 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 (ε 0 /ε F > 1) the spectrum is continuous and has the Bogolubov form, but in the weak-coupling limit (ε 0 /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/ξ 0 (where ξ 0 is the Cooper pair size), and (ii) pair excitations with q ≃ (8 m μ) 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 ε 0 /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 ξ 0 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 F ξ 0 ≃1, where k F is the Fermi momentum.

Meera M. Parish