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arXiv:cond-mat/9508076

On the normal phase of 2D Fermi liquid with weak attraction between particles

V. P. Gusynin, В. М. Локтев, Igor A. Shovkovy

Published Aug 18, 1995• 0 citations

Abstract

Proceeding from the simplest field theoretical model of 2D metal, the normal phase Green functions of the weakly interacting fermions and the order parameter fluctuations (responsible for the attraction between fermions) are obtained. It is shown that taking into consideration the fluctuations mentioned leads to a considerable reduction of the fermion wave function renormalization constant (quasiparticle weight) as well as to a linear dependence of the quasiparticle damping on the temperature. A general dependence of 2D Fermi liquid properties on the fermion density is discussed. The relevance of the proposed model to the marginal behavior of the Fermi liquid of high--$T_c$ superconductors, in particular, to their linear temperature dependence of the resistivity is indicated.

DOI: 10.48550/arxiv.cond-mat/9508076

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Proceeding from the simplest field theoretical model of 2D metal, the normal phase Green functions of the weakly interacting fermions and the order parameter fluctuations (responsible for the attraction between fermions) are obtained. It is shown that taking into consideration the fluctuations mentioned leads to a considerable reduction of the fermion wave function renormalization constant (quasiparticle weight) as well as to a linear dependence of the quasiparticle damping on the temperature. A general dependence of 2D Fermi liquid properties on the fermion density is discussed. The relevance of the proposed model to the marginal behavior of the Fermi liquid of high--

T_c

superconductors, in particular, to their linear temperature dependence of the resistivity is indicated.

The effect of static fluctuations in the phase of the order parameter on the normal and superconducting properties of a 2D system with attractive four-fermion interaction has been studied. Analytic expressions for the fermion Green function, its spectral density and the density of states are derived. The resultant single-particle Green function clearly demonstrates non-Fermi liquid behavior. The results show that as the temperature increases through the 2D critical temperature the width of the quasiparticle peaks broadens significantly. At the same time one retains the gap in quasiparticle spectrum. The spectral density for the dynamical fluctuations can also be obtained. Clearly the dynamical fluctuations fill the gap giving the observed pseudogap behaviour.

The effect of static fluctuations in the phase of the order parameter on the normal and superconducting properties of a 2D system with attractive four-fermion interaction has been studied. Analytic expressions for the fermion Green function, its spectral density and the density of states are derived. The resultant single-particle Green function clearly demonstrates non-Fermi liquid behavior. The results show that as the temperature increases through the 2D critical temperature the width of the quasiparticle peaks broadens significantly. At the same time one retains the gap in quasiparticle spectrum. The spectral density for the dynamical fluctuations can also be obtained. Clearly the dynamical fluctuations fill the gap giving the observed pseudogap behaviour.

The effect of static fluctuations in the phase of the order parameter on the normal and superconducting properties of a 2D system with attractive four-fermion interaction is studied. Analytic expressions for the fermion Green’s function, its spectral density, and the density of states are derived in the approximation where the coupling between the spin and charge degrees of freedom is neglected. The resulting single-particle Green’s function clearly demonstrates a non-Fermi-liquid behavior. The results show that as the temperature increases through the 2D critical temperature, the widths of the quasiparticle peaks broaden significantly.

By means of the Fermi-liquid approach, the effects of exchange and correlations are considered in a layered two-dimensional electron gas. A graphical derivative technique is introduced to obtain the contributions to the interparticle interactions from different channels. It is shown that the interaction in the particle - hole channel can induce the metal - insulator phase transition when the Fermi momentum is comparable with the inverse interlayer spacing, . It is also shown that the Cooper-like scattering processes give rise to the scaling of the Fermi liquid response as Im , which leads to the linear temperature dependence of the quasiparticle damping. The possibility of superconductivity in the region between the insulator and normal metal phases, accounting for the particle - hole excitations, is discussed. The effect of the spin fluctuations on the superconductivity due to the particle - hole excitations is also considered.