Flux quantization experiments indicate that the carriers, Cooper pairs
(pairons), in the supercurrent have charge magnitude 2e, and that they move
independently. Josephson interference in a Superconducting Quantum Interference
Device (SQUID) shows that the centers of masses (CM) of pairons
move as bosons with a linear dispersion relation. Based on this evidence we
develop a theory of superconductivity in conventional and materials
from a unified point of view. Following Bardeen, Cooper and Schrieffer
(BCS) we regard the phonon exchange attraction as the cause of superconductivity.
For cuprate superconductors, however, we take account of both
optical- and acoustic-phonon exchange. BCS started with a Hamiltonian
containing “electron” and “hole” kinetic energies and a pairing interaction
with the phonon variables eliminated. These “electrons” and “holes” were
introduced formally in terms of a free-electron model, which we consider
unsatisfactory. We define “electrons” and “holes” in terms of the curvatures
of the Fermi surface. “Electrons” (1) and “holes” (2) are different
and so they are assigned with different effective masses: Blatt,
Schafroth and Butler proposed to explain superconductivity in terms of a
Bose-Einstein Condensation (BEC) of electron pairs, each having mass M
and a size. The system of free massive bosons, having a quadratic dispersion
relation: and moving in three dimensions (3D) undergoes a
BEC transition at where is the pair density.
This model met difficulties because the interpair separation estimated from
this formula is much smaller than the experimental pair size (~ Å for
Pb), and hence these pairs cannot be regarded as free moving. We show
from first principles that the CM of pairons move as bosons with a linear
dispersion relation: ,where is a pairon ground-state energy,
and
velocity. The systems of free pairons, moving with the linear dispersion relation,
undergo a BEC in 3D and 2D. The critical temperature is given by
The interpairon distance
is several times greater than the BCS pairon
size Hence the BEC occurs without the pairon overlap,
which justifies the notion of free pairon motion. The superconducting
transition will be regarded as a BEC transition. In the currently predominant
BCS theory the superconducting temperature is identified as the
vi
temperature at which the stationary (zero-momentum) pairons break up and
disappear in the system. But the electronic heat capacity in
has a maximum at with a shoulder above which can only be explained
naturally in terms of a model in which many pairons participate in the phase
transition with no dissociation. (No feature above is predicted by the
BCS theory.) The dissociation take place one by one just as hydrogen molecules
break up in a gas mixture of H). In the B-E condensation
a great number of pairons cooperatively participate and exhibit a macroscopic
change of phase. Hence in our view the pairons do not break up at
Above pairons move independently in all allowed directions and they
contribute to the resistive conduction. Below condensed pairons move
without resistance, following the quantum laws described in terms of the
Ginzburg-Landau wavefunction. Non-condensed pairons, unpaired electrons
and quantum vortices contribute to the normal resistive conduction