Superconducting Condensate Formation in Metallic Systems With Arbitrary Carrier Density

Abstract

This article gives a contemporary and to some extent pedagogical review of the current theoretical understanding of the formation of the superconducting state in metallic systems with a variable density of carriers. We make an attempt to describe the crossover from the Bose-Einstein condensation type (small densities) to the Bardeen-Cooper-Schrieffer one (large densities). The functional methods are used throughout the treatment. The most of the results are considered in a review form for the first time. Some of them (in particular, the possible opening of a pseudogap) are used to explain the experimental data avaliable for high-temperatures superconductors.

Hopping anisotropies: A candidate for BCS-BEC crossover

“…The similarity has often led these quantities to be considered indistinguishable. 12 However, they are different quantities and the difference is very conspicuous in the BEC regime. As for a BCS superconductor, the two length scales are very similar and have values much larger than the interparticle spacing and close to បv F ⌬ , the well-known Pippard result.…”

“…In this way, the system consists of Bose-Einstein ͑BE͒ condensate of bosons and the gap in the quasiparticle spectrum is different than that of BCS theory. 12,23 In this paper, we study a simple model that incorporates anisotropy in the hopping frequencies of the charge carriers. In a two-dimensional t-J-U model, this means that the kinetic energies are different in the x and y directions ͑i.e., t x t y ͒; however, the charges are allowed to interact via an isotropic exchange J.…”

“…To be more specific, the appearance of a pseudogap in the form of a depletion of single-particle spectral weight around the fermi level below a certain critical temperature T * in the underdoped regime of cuprates [12][13][14][15][16][17][18] demonstrates the most comprehensive deviation from the mean-field ͑BCS͒ scenario for superconductors. The BCS picture may be viewed as a very special case where the pair formation and the condensation occur simultaneously; i.e., at the same temperature while at moderate values of the interaction strength, the pairs form and condense at different temperatures, as energetics favor pair formation within the normal phase.…”

On Temperature Versus Doping Phase Diagram of High Critical Temperature Superconductors

“…As it can be seen from the previous Section (see also Refs. [9,11]) there exist two characteristic temperatures in a system: T ρ , where formally the complete order parameter given by Eq. (5) arises but its phase is a random quantity, i.e.…”

Superconducting condensate formation in quasi-2D systems with arbitrary carrier density

“…It is widely accepted [1][2][3][4][5][6] that the formation of the superconducting state in high-temperature superconductors (HTSCs) is quite different from traditional superconductors. The strongly anisotropic, almost twodimensional, structure of HTSCs compounds increases significantly the influence of fluctuations and the different types of order appear to be separated on different energy scales.…”