  Developing a theory of high-temperature superconductivity in copper oxides is
one of the outstanding problems in physics. It is a challenge that has defeated
theoretical physicists for more than twenty years. Attempts to understand this
problem are hindered by the subtle interplay among a few mechanisms and the
presence of several nearly degenerate and competing phases in these systems.
Here we present some crucial experiments that place essential constraints on
the pairing mechanism of high-temperature superconductivity. The observed
unconventional oxygenisotope effects in cuprates have clearly shown strong
electron-phonon interactions and the existence of polarons and/or bipolarons.
Angle-resolved photoemission and tunneling spectra have provided direct
evidence for strong coupling to multiple-phonon modes. In contrast, these
spectra do not show strong coupling features expected for magnetic resonance
modes. Angle-resolved photoemission spectra and the oxygen-isotope effect on
the antiferromagnetic exchange energy J in undoped parent compounds
consistently show that the polaron binding energy is about 2 eV, which is over
one order of magnitude larger than J = 0.14 eV. The normal-state
spin-susceptibility data of holedoped cuprates indicate that intersite
bipolarons are the dominant charge carriers in the underdoped region while the
component of Fermi-liquid-like polarons is dominant in the overdoped region.
All the experiments to test the gap or order-parameter symmetry consistently
demonstrate that the intrinsic gap (pairing) symmetry for the Fermi-liquid-like
component is anisotropic s-wave and the order-parameter symmetry of the
Bose-Einstein condensation of bipolarons is d-wave.
