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Modern Physics Letters B

An Effective Low-Energy Quasiparticle Model with Attractive Interaction

A. Ferraz, Y. Ohmura

Published Nov 10, 1998• 0 citations
Publisher

Abstract

We consider the "high-energy" single-particle states of a strongly interacting electron liquid. These states should be taken into account whenever there are strong incoherent effects produced by interactions. Considering the presence of these particles which are confined in a thin shell in momentum space around [Formula: see text] as well as "low-energy" quasiparticles we derive an effective model by integrating out the "high-energy" fields. The resulting theory produces an effective interaction for the quasiparticles which may be large and negative. This produces an instability which drives the electron liquid towards superconductivity or another non-perturbative regime.

DOI
10.1142/s0217984998001220

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We consider the "high-energy" single-particle states of a strongly interacting electron liquid. These states should be taken into account whenever there are strong incoherent effects produced by interactions. Considering the presence of these particles which are confined in a thin shell in momentum space around [Formula: see text] as well as "low-energy" quasiparticles we derive an effective model by integrating out the "high-energy" fields. The resulting theory produces an effective interaction for the quasiparticles which may be large and negative. This produces an instability which drives the electron liquid towards superconductivity or another non-perturbative regime.
One considers the superfluid (SF) state of a Bose liquid with a strong repulsion between bosons, in which at T=0, along with a weak single-particle Bose-Einstein condensate (BEC), there exists an intensive pair coherent condensate (PCC), analogous to the Cooper condensate in a Fermi liquid with an attraction between the fermions. Such a PCC emerges in a system of bosons due to an oscillating sign-changing momentum dependence of the Fourier component of the pair interaction potential, which is characteristic of a certain family of repulsion potentials. In such cases, the Fourier component is negative in some domain of nonzero momentum transfer, which corresponds to an effective attraction. The collective effects of renormalization (``screening'') of the initial interaction lead to a suppression of the repulsion and an enhancement of the effective attraction. It is the ratio of the BEC density to the full density of the liquid n0/n≪1n_0/n\ll 1n0​/n≪1 that is used as a small parameter---unlike in the Bogolyubov theory for a quasi-ideal Bose gas, in which the small parameter is the ratio of the number of supracondensate excitations to the number of particles in an intensive BEC, (n−n0)/n0≪1(n-n_0)/n_0\ll 1(n−n0​)/n0​≪1. A closed system of nonlinear integral equations for the normal and anomalous self-energy parts is obtained, in the framework of a renormalized perturbation theory built on combined hydrodynamic and field variables. In the framework of the hard-spheres model, a spectrum of quasiparticles is obtained, which is in good accordance with the experimental spectrum of elementary excitations in superfluid 4^44He. The question of applicability of the Landau criterion in the absence of quantum vortices is discussed.
Abstract Dedicated to Bernhard Mühlschlegel on the occasion of his 80th birthday We address the question, whether low lying one‐particle excitations in the Fermi‐liquid phase of highly correlated electron systems can form well defined bands of nearly stable quasiparticles, and comment on features of a universal band picture for these systems. We outline how to derive a description of instabilities to magnetic, charged ordered or superconducting phases, which bears a close analogy to Stoner theory and lends itself to an interpretation in terms of quasiparticle bands and residual interactions at low temperatures. Concepts and problems are illustrated via calculations for some standard models of solid‐state theory using modern many‐body techniques like NRG, NCA and DMFT. Differences to conventional band structure theory are pointed out. We shortly comment on the relevance of these questions to the physics of inhomogeneous systems and small particles.
Conditions at which a quasi-one-dimensional (1D) electron system can be considered as a quantum liquid of impenetrable charged particles are theoretically analyzed. In the presence of an inert, neutralizing background, a motion of impenetrable electrons is shown to expose a positive charge, resulting in an effective mutual attraction of infinite range. As a result, all electrons are involved in the long-range pairing. A model of spinless fermions with infinitesimal attraction of infinite range is proposed to describe the excitation spectrum and the superconducting gap in low-density 1D electron channels. In contrast with the conventional theory, the energy gap does not contain exponentially small factors. It depends mostly on the Coulombic parameters of the system, which guides practical aspects of high-temperature superconductivity.
A model to describe electronic correlations in energy bands is considered. The model is a generalization of the conventional Hubbard model that allows for the fact that the wave function for two electrons occupying the same Wannier orbital is different from the product of single-electron wave functions. We diagonalize the Hamiltonian exactly on a four-site cluster and study its properties as a function of band filling. The quasiparticle weight is found to decrease and the quasiparticle effective mass to increase as the electronic band filling increases, and spectral weight in one- and two-particle spectral functions is transferred from low to high frequencies as the band filling increases. Quasiparticles at the Fermi energy are found to be more ``dressed'' when the Fermi level is in the upper half of the band (hole carriers) than when it is in the lower half of the band (electron carriers). The effective interaction between carriers is found to be strongly dependent on band filling becoming less repulsive as the band filling increases and attractive near the top of the band in certain parameter ranges. The effective interaction is most attractive when the single-hole carriers are most heavily dressed, and in the parameter regime where the effective interaction is attractive, hole carriers are found to ``undress,'' hence become more like electrons, when they pair. It is proposed that these are generic properties of electronic energy bands in solids that reflect a fundamental electron-hole asymmetry of condensed matter. The relation of these results to the understanding of superconductivity in solids is discussed.
In contrast to the well-known Fermi-liquid theory of three dimensions, interacting one-dimensional and quasi-one-dimensional systems of fermions are described at low energy by an effective theory known as Luttinger liquid theory. This theory is expressed in terms of collective many-body excitations that show exotic behavior such as spin-charge separation. Luttinger liquid theory is commonly applied on the premise that ``low energy'' describes both the spin and charge sectors. However, when the interactions in the system are very strong, as they typically are at low particle densities, the ratio of spin to charge energy may become exponentially small. It is then possible at very low temperatures for the single-spin excitation energy to be low compared to the characteristic single excitation charge energy, but still high compared to the characteristic spin energy. This energy window of near ground-state charge degrees of freedom but highly thermally excited spin degrees of freedom is called a spin-incoherent Luttinger liquid. The spin-incoherent Luttinger liquid exhibits a higher degree of universality than the Luttinger liquid and its properties are qualitatively distinct. In this Colloquium some recent theoretical developments in the field are detailed and experimental indications of such a regime in gated semiconductor quantum wires are described.
A strongly coupled many-body system (a system of fermions confined in a shell surrounding the Fermi surface for which the variation in the single-particle kinetic energy is neglected) is defined. Some general properties of this system are obtained, in particular a criterion for permissible approximations. It is shown that a set of diagrams in which an electron of momentum $\ensuremath{-}\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$ and of spin \ensuremath{\downarrow} interacts with many electrons of momentum $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}+\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}$ and spin \ensuremath{\uparrow}, where $\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}$ does not grow too large, can be consistently extracted from the totality of graphs generated by this strongly coupled Hamiltonian. When analyzed, these lead to a ground-state and single-particle spectrum displaying the important qualitative features of a BCS superconductor.