The BCS-Bose crossover theory
Por:
Adhikari S.K., de Llano M., Sevilla F.J., Solís M.A., Valencia J.J.
Publicada:
1 ene 2007
Resumen:
We contrast four distinct versions of the BCS-Bose statistical crossover theory according to the form assumed for the electron-number equation that accompanies the BCS gap equation. The four versions correspond to explicitly accounting for two-hole-(2h) as well as two-electron-(2e) Cooper pairs (CPs), or both in equal proportions, or only either kind. This follows from a recent generalization of the Bose-Einstein condensation (GBEC) statistical theory that includes not boson-boson interactions but rather 2e- and also (without loss of generality) 2h-CPs interacting with unpaired electrons and holes in a single-band model that is easily converted into a two-band model. The GBEC theory is essentially an extension of the Friedberg-Lee 1989 BEC theory of superconductors that excludes 2h-CPs. It can thus recover, when the numbers of 2h- and 2e-CPs in both BE-condensed and non-condensed states are separately equal, the BCS gap equation for all temperatures and couplings as well as the zero-temperature BCS (rigorous-upper-bound) condensation energy for all couplings. But ignoring either 2h- or 2e-CPs it can do neither. In particular, only half the BCS condensation energy is obtained in the two crossover versions ignoring either kind of CPs. We show how critical temperatures Tc from the original BCS-Bose crossover theory in 2D require unphysically large couplings for the Cooper/BCS model interaction to differ significantly from the Tcs of ordinary BCS theory (where the number equation is substituted by the assumption that the chemical potential equals the Fermi energy). © 2007.
Filiaciones:
Adhikari S.K.:
Instituto de Física Teórica, UNESP - São Paulo State University, 01405-900 São Paulo, SP, Brazil
de Llano M.:
Texas Center for Superconductivity, University of Houston, Houston, TX 77204, United States
Instituto de Investigaciones en Materiales, Universidad Nacional Autónoma de México, 04510 México, DF, Mexico
Consortium of the Americas for Interdisciplinary Science, University of New Mexico, Albuquerque, NM 87131, United States
Sevilla F.J.:
Instituto de Física, UNAM, 01000 México, DF, Mexico
Consortium of the Americas for Interdisciplinary Science, University of New Mexico, Albuquerque, NM 87131, United States
Solís M.A.:
Instituto de Física, UNAM, 01000 México, DF, Mexico
Valencia J.J.:
Instituto de Investigaciones en Materiales, Universidad Nacional Autónoma de México, 04510 México, DF, Mexico
Universidad de la Ciudad de México, San Lorenzo Tezonco, 09940 México, DF, Mexico
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