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arXiv:cond-mat/0305162

Superconducting properties of the 2D models with different types of inter-particle coupling

В. М. Локтев, Volodymyr Turkowski

Published May 8, 2003• 0 citations
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Abstract

The superconducting properties of the 2D fermion system with local and different types of the indirect boson-exchange attractions in the cases of s-wave and d-wave pairing are reviewed and analysed at T=0. In particular, the possibility of the crossover from the Bose-Einstein condensation regime to the BCS-like superconductivity with the carrier density and coupling changing in the case of different pairing channels is discussed. Gaussian fluctuations of the order parameter are taken into account and the carrier density dependence of the gap is studied in this case. The role of the interaction form in the physical behavior of the systems is also discussed.

DOI
10.48550/arxiv.cond-mat/0305162

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arXiv:cond-mat/9906180•Physical review. B, Condensed matter•May 1, 2000•74 citations
The superconducting properties of the 2D fermion system with local and different types of the indirect boson-exchange attractions in the cases of s-wave and d-wave pairing are reviewed and analysed at T=0. In particular, the possibility of the crossover from the Bose-Einstein condensation regime to the BCS-like superconductivity with the carrier density and coupling changing in the case of different pairing channels is discussed. Gaussian fluctuations of the order parameter are taken into account and the carrier density dependence of the gap is studied in this case. The role of the interaction form in the physical behavior of the systems is also discussed.
The superconducting properties of a two-dimensional metallic system with arbitrary carrier density and both local and various types of attractive indirect boson-exchange interaction in the cases of s- and d-wave pairing are analyzed and reviewed at T=0. In particular, the possibility of a crossover from the Bose–Einstein condensation regime to Bardeen–Cooper–Schrieffer-like superconductivity with growing carrier density and changing coupling in the case of different pairing channels is discussed. Gaussian fluctuations of the order parameter are taken into account, and the carrier density dependence of the gap magnitude is studied. The role of the form of the interparticle attractive interaction in the physical behavior of the system is also considered.
Using the microscopic model Hamiltonian, the equations for order parameter and chemical potential have been obtained for a system of Fermi-particles interacting with phonons which permit an analysis of its superconducting properties to be made for an arbitrary fermion concentration. The solution of the equations is given that makes it possible to trace the crossover from a local pair regime to Cooper pairing. The type of superconducting behavior is shown to depend on both the position of the Fermi level with respect to a maximum phonon energy and strength of indirect interactions between fermions.
The two component model of coexisting local electron pairs and itinerant fermions coupled via charge exchange mechanism, which mutually induces superconductivity in both subsystems, is discussed. The cases of isotropic s-wave and anisotropic pairing of extended s and d x 2 −y 2-wave symmetries are analyzed for a 2D square lattice within the BCS-mean field approximation and the Kosterlitz-Thouless theory. We determined the phase diagrams and superconducting characteristics as a function of the position of the local pair (LP) level and the total electron concentration. The model exhibits several types of interesting crossovers from BCS like behavior to that of LP’s. Some of our results are discussed in connection with a two-component scenario of preformed pairs and unpaired electrons for exotic superconductors. Key words: Boson-Fermion model, Phase fluctuations A system of interacting charged bosons (bound electron pairs) and electrons can show features which are intermediate between those of local pair superconductors and those of classical BCS systems. Such a two component (bosonfermion) model is of relevance for high temperature superconductors (HTS) and other exotic superconductors [1,2,3,4,5,6,7,8,9,10]. Recently, we have studied a generalization of this model to the case of anisotropic pairing [9,10]. Here, we shortly outline the study and present further results concerning the phase diagrams and superconducting properties of such a system in the case of isotropic s-wave pairing as well as for anisotropic pairings of d- and extended s-wave symmetries, for a 2D square lattice.
Proceeding from a microscopic model Hamiltonian for a system of Fermi particles with attraction, we have derived an effective Lagrangian, which allows analysis of the superconducting properties of the system for arbitrary fermion concentrations. Exact solution of the equations for the gap and the chemical potential enables us to examine the crossover from the regime of local pairs and superfluidity to the Cooper pairing and the BCS-like superconductivity. It is shown that the physical parameter that demarcates the regions of exotic and normal behavior is the fermion bound state energy. The expressions derived suggest that in the region of relatively low concentrations the parameters of a 2D metal correspond to a type-II superconductor.
Physical properties of two-dimensional (2D) superconductors is an active area of long time researches in which many, even principle, questions are still open. One of them is a possibility of a smooth crossover of the system from the standard Bardeen–Cooper–Schrieffer (BCS) regime of strongly overlapping Cooper pairs to the regime of Bose–Einstein condensation (BEC) of almost non-overlapping local pairs. The adequate to the real process description of this transition which can happen either by changing the doping or temperature would lead to a better understanding of the superconducting properties of materials. Though the crossover is not observed in one of the most important layered systems—namely, cuprate superconductors—we demonstrate that in systems with stronger electron-electron attraction it is possible. In particular, in the d-wave channel at sufficiently high doping the crossover can take place with growth of temperature two times, i.e., as BEC→BCS, and followed by reverse BCS→BEC condensation. The physical mechanisms of such transitions and possibility to detect them experimentally in real systems are discussed.
In this paper we study the BCS Bose-Einstein condensation (BEC) crossover scenario within the superconducting state, using a T-matrix approach which yields the ground state proposed by Leggett. Here we extend this ground state analysis to finite temperatures T and interpret the resulting physics. We find two types of bosoniclike excitations of the system: long lived, incoherent pair excitations and collective modes of the superconducting order parameter, which have different dynamics. Using a gauge invariant formalism, this paper addresses their contrasting behavior as a function of T and superconducting coupling constant g. At a more physical level, our paper emphasizes how, at finite T, BCS-BEC approaches introduce an important parameter ${\ensuremath{\Delta}}_{\mathrm{pg}}^{2}={\ensuremath{\Delta}}^{2}\ensuremath{-}{\ensuremath{\Delta}}_{\mathrm{sc}}^{2}$ into the description of superconductivity. This parameter is governed by the pair excitations and is associated with particle-hole asymmetry effects that are significant for sufficiently large g. In the fermionic regime, ${\ensuremath{\Delta}}_{\mathrm{pg}}^{2}$ represents the difference between the square of the excitation gap ${\ensuremath{\Delta}}^{2}$ and that of the superconducting order parameter ${\ensuremath{\Delta}}_{\mathrm{sc}}^{2}.$ The parameter ${\ensuremath{\Delta}}_{\mathrm{pg}}^{2},$ which is necessarily zero in the BCS (mean field) limit increases monotonically with the strength of the attractive interaction g. It follows that there is a significant physical distinction between this BCS-BEC crossover approach (in which g is the essential variable which determines ${\ensuremath{\Delta}}_{\mathrm{pg}})$ and the widely discussed phase fluctuation scenario in which the plasma frequency is the tuning parameter. Finally, we emphasize that in the strong coupling limit, there are important differences between the composite bosons that arise in crossover theories and the usual bosons of the (interacting) Bose liquid. Because of constraints imposed on the fermionic excitation gap and chemical potential, in crossover theories, the fermionic degrees of freedom can never be fully removed from consideration.