A generalized BEC picture of superconductors

Abstract

A recent re‐examination of BCS theory leads one to devise a generalized BEC formalism (GBEC), that is, essentially a boson‐fermion (BF) model containing three new ingredients: (i) Cooper pairs (CPs), in contrast to BCS pairs, as real bosons; (ii) BF vertex interactions (analogous to electron‐phonon vertices); and (iii) two‐hole CPs (2hCPs) accounted for along with two‐electron CPs (2eCPs). In addition to the usual normal phase at high‐enough temperatures T, three condensed phases emerge at lower temperatures with substantially higher Tcs than BCS theory. These are: two pure BEC phases of 2eCPs and of 2hCPs as well as a mixed phase with both kinds of CPs. BCS theory is precisely recovered with a mixed phase of equal numbers of both kinds of CPs. In contrast to the well‐known BCS exponential rise from zero of Tc as function of carrier‐number density the GBEC scheme exhibits the linear rise as function of doping as eminently observed in high‐Tc underdoped superconductors such as YBCO. © 2012 Wiley Periodicals, Inc.

Multicondensate Superconductivity in a Generalized BEC Formalism with Hole Cooper Pairs

“…Three crucial elements characterizing GBEC are (i) CPs, which obey Bose statistics [13], are considered as real bosons-as opposed to BCS pairs which are strictly not bosonic as they do not obey Bose commutation relations [3]; (ii) BF vertex interactions (similar to electron-phonon vertices) which drive formation/disintegration of CPs; and (iii) 2h-CPs explicitly accounted for along with two-electron (2e) CPs. Besides, including as special cases, all known statistical models of superconductors [9][10][11][12][13] the GBEC formalism also subsumes the BCS-Bose "crossover" [11] theory which in turn includes BCS as a special case.…”

“…Besides, including as special cases, all known statistical models of superconductors [9][10][11][12][13] the GBEC formalism also subsumes the BCS-Bose "crossover" [11] theory which in turn includes BCS as a special case.…”

“…A newer approach, based on a ternary BF model with explicit inclusion of two-hole (2h) Cooper pairs (CPs) leads to a formalism that generalizes Bose-Einstein condensation (GBEC) [9][10][11][12][13] and is vastly more general with sizeable increases in T c with respect to those predicted by BCS. The ternary-BF-gas [4,[6][7][8][13][14][15] GBEC formalism subsumes BCS theory as well as ordinary BEC [16,17] and was proposed to describe SC in general.…”

“…The ternary-BF-gas [4,[6][7][8][13][14][15] GBEC formalism subsumes BCS theory as well as ordinary BEC [16,17] and was proposed to describe SC in general.…”

BCS-Bose crossover theory extended with hole Cooper pairs

“…Boson-fermion (BF) models of SCs as a BEC go back to the mid-1950s 11,13 predating even the BCS-Bogoliubov theory. all BF models neglect the explicit effect of hole CPs included on an equal footing with electron CPs to give a complete BF model [16][17][18] which we here call the GBEC theory. This enables one to easily deal with nonzero T .…”