Screening effects in superconductors

Abstract

The partition function of the Hubbard model with local attraction and long range Coulomb repulsion between electrons is written as a functional integral with an action $A$ involving a pairing field $\Delta$ and a local potential $V$. After integration over $V$ and over fluctuations in $|\Delta|^{2}$, the final form of $A$ involves a Josephson coupling between the local phases of $\Delta$ and a "kinetic energy" term, representing the screened Coulomb interaction between charge fluctuations. The competition between Josephson coupling and charging energy allows to understand the relation between $T_{C}$ and composition in high-$T_{C}$ materials, in particular superlattices, alloys and bulk systems of low doping.Comment: 4 pages, revtex, no figures, submitted to Physica B (Proceedings of SCES '96 International Conference, held in Zurich from 19th to 21st of August

Persistence of pseudogap formation in quasi-2D systems with arbitrary carrier density

“…The analytical and numerical investigation of the systems (19), (25), (24) and (26), (27) yield the following results.…”

“…Surprisingly α even decreases as the carrier density increases. For this reason one can indeed use the equation (19) to determine T q BKT . Therefore one expects the results obtained for the pure 2D model to persist to the quasi-2D case.…”

“…In contrast to the usual method where one calculates Z in terms of the Φ(x) and Φ * (x) variables, the parameterisation Φ(x) = ρ(x) exp [−iθ(x)] should be used [8] (see also [18,19]). In addition to this reparameterisation one must make the replacement ψ σ (x) = χ σ (x) exp [iθ(x)/2].…”

“…Thus, in practice, we will solve numerically the system of equations (19), (25) and (24) to study T q BKT as a function of n f . Setting ρ = 0 in the equations (23) and (24), we arrive (in the same approximation) at the equations for the critical temperature T ρ above which ρ = 0 and the corresponding value of µ:…”

Pseudogap phase formation in the crossover from Bose-Einstein condensation to BCS superconductivity

“…In contrast to the usual method for calculating Z in Φ, Φ * variables, the parametrization Φ(x) = ρ(x) exp [−iθ(x)] is more appropriate for presenting the corresponding integral in two dimensions [22] (see also Refs. [23] and [24]). When this replacement by modulus-phase variables is implemented, it is evident that one must also replace ψ σ (x) = χ σ (x) exp [iθ(x)/2].…”