  A model for high temperature superconductors based on the idea of Cooper
pairs comprised of electrons from different bands is studied. We propose that
the two bands relevant for the cuprates are comprised of Cu dx2-y2, dz2, planar
O psigma, and apical O pz orbitals. Along the diagonal, kx=ky in the Brillouin
zone, the two band Fermi surfaces may cross. We associate the optimal doping
for the highest Tc with this point because only in the vicinity of this
touching point are inter-band Cooper pairs energetically possible. Due to the
lack of time reversal invariance of an inter-band Cooper pair with itself, the
standard interpretation of Josephson tunneling is altered such that the
detailed nature of the single particle tunneling matrix elements contributes to
the supercurrent. The dx2-y2 gap observations from Josephson tunneling are
shown to arise from our model with pairing due to phonons. A Hubbard model is
written down for the two bands at the Fermi energy with realistic parameters
for LaSrCuO. The anomalous normal state features in the nmr are calculated and
qualitatively explained as due to the character of the two bands in the
vicinity of the crossing point. The Hall effect is calculated using standard
Bloch-Boltzmann transport theory. The observed strong temperature dependence of
the Hall coefficient is reproduced and is due to the strong reshaping of the
current carrying band Fermi surface due to band repulsion with the other band
for dopings very close to the Fermi surface touching point. Reasonable
quantitative agreement is also obtained for the nmr and Hall effect. A linear
resistivity at optimal doping is expected due to the proximity of the second
band in k space which can strongly relax the current and the "smallness" of the
current carrying Fermi surface.

Superconductivity;Materials Science