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A recent theoretical breakthrough [1]-[3] generalizes the BCS theory
of superconductivity in a fundamental way by unifying the 1957 BCS
theory with the 1925 theory of Bose-Einstein condensation (BEC). It
gives [4] roughly good first-principles Tc predictions for exotic
as well as conventional superconductors---without abandoning the phonon
interaction mechanism. It also allows for room temperature superconductivity
with the same dynamical mechanism. The only condition is that one
depart moderately from the perfect electron (e)-/hole (h)-Cooper-pair
(CP) symmetry to which BCS is restricted by construction, and ideally
that there be many more hole (pre-formed?) CPs compared with electron
CPs just above Tc. Thus, one might explain why largely all superconductors
empirically have substantially higher Tc's if their normal-state single-charge
carriers are holes rather than electrons. The new theory reduces in
the appropriate special cases to: a) ordinary BCS theory, which has
perfect 2e/2h-CP symmetry [i.e., equal numbers of 2e- and 2h-CPs below
and above Tc], under weak inter-fermionic coupling; b) the somewhat
more general BCS-Bose crossover picture dating back to Friedel et
al. in 1967; c) a 1989 boson-fermion (BF) BEC model by T.D. Lee et
al. of superconductors, but without 2h-CP carriers and thus unrelated
to BCS theory; d) a recent ideal BF binary-gas model predicting nonzero
BEC Tc's even in 2D; and e) ordinary BEC (1925) for no 2h-CPs, as
the number of unpaired electrons vanishes in the original BF mixture.
The new theory is essentially a BF statistical model similar to those
developed in the mid-50's by Schafroth, Blatt & Butler (SBB) but
which now includes 2h-CPs on an equal footing with 2e-CPs, and which
unlike the SBB models allows for the fermionic energy gap. The prospect
of engineering superconductors to have much larger Tc's than presently
will thus require, to begin with, devising measurements of the charge
sign of CPs at or just above Tc. [1] V.V. Tolmachev, Phys. Lett. A
266, 400 (2000). [2] M. Fortes, M.A. Sol�, M. de Llano & V.V.
Tolmachev, Physica C 364, 95 (2001). [3] M. de Llano & V.V. Tolmachev,
Physica A 317, 546 (2003). [4] J. Batle, M. Casas, M. Fortes, M. de
Llano, O. Rojo, F.J. Sevilla, M.A. Sol� & V.V. Tolmachev, Cond.
Matter Theories 18, xxx (2003)BCS and BEC finally unified: A brief
review. cond-mat/0211456.
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