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On Unconventional Electron Pairing In a Periodic Potential
Abstract
On the assumption that two electrons with the same group velocity effectively
attract each other a simple model Hamiltonian is proposed to question the
existence of unconventional electron pairs formed by electrons in a strong
periodic potential.
We study possible quantum states of two correlated electrons in a two-dimensional periodic potential and find a metastable energy band of electron pairs between the two lowest single-electron bands. These metastable states result from interplay of the electron-electron Coulomb interaction and the strength of the crystal potential. The paired electrons are bound in the same unit cell in relative coordinates with an average distance between them of approximately one third of the crystal period. Furthermore, we discuss how such electron pairs can possibly be stabilized in a many-electron system.
A nonrelativistic treatment is given of electron-electron scattering in the presence of a laser field. The field is accounted for by the external field approximation and is represented by a circularly polarised monochromatic plane-wave field. A simple analytic expression is derived for the transition amplitude, which is shown to exhibit internal resonances as well as intensity-dependent shifts. The former is the nonrelativistic limit of the resonant Moller scattering predicted previously by Oleinik (1967). The latter, however, appears in a higher order of v/c and is consequently negligible for very slow electrons. The differential cross section of the scattering is also given where the effect of the spin and symmetry is teken into account explicitly. The width of resonances is introduced phenomenologically but its connection with previous methods is established. Consideration is also given to the experimental conditions under which the effects may become observable.
From recent Hall effect measurements and angle-resolved photo-emission spectroscopy the interesting picture emerges of co-existing hole- and electron-like quasiparticle bands, both in electron- and hole-doped superconducting cuprates. We reflect on the idea that bosonic electron-hole pairs may be formed in the cuprates and on the possibility that these pairs undergo Bose-Einstein condensation. The relevance to high-T-c superconductivity in the cuprates will be discussed. (c) 2005 Elsevier B.V. All rights reserved.
Metallic, oxygen-deficient compounds in the Ba–La–Cu–O system, with the composition Ba
x
La5–x
Cu5O5(3–y) have been prepared in polycrystalline form. Samples withx=1 and 0.75,y>0, annealed below 900C under reducing conditions, consist of three phases, one of them a perovskite-like mixed-valent copper compound. Upon cooling, the samples show a linear decrease in resistivity, then an approximately logarithmic increase, interpreted as a beginning of localization. Finally an abrupt decrease by up to three orders of magnitude occurs, reminiscent of the onset of percolative superconductivity. The highest onset temperature is observed in the 30 K range. It is markedly reduced by high current densities. Thus, it results partially from the percolative nature, bute possibly also from 2D superconducting fluctuations of double perovskite layers of one of the phases present.
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