We have calculated the tunneling conductance of a superconductor-insulator-superconductor junction based on the polaron-bipolaron theory of superconductivity. The predicted incoherent hump features are in quantitative agreement with tunneling spectra of optimally doped Bi2Sr2CaCu2O8+y and Bi2Sr2Ca2Cu3O10+y. We further show that angle-resolved photoemission spectra of underdoped cuprates are consistent with the Bose-Einstein condensation of inter-site bipolarons and that the superconducting gap symmetry is d-wave, which is determined by the anomalous kinetic process rather than by the pairing interaction. In the overdoped cuprates (BCS-like superconductors), the superconducting gap symmetry is the same as the pairing symmetry, which is found to be extended s-wave with eight line nodes in hole-doped cuprates and nodeless s-wave in electron-doped cuprates. The polaronic effect significantly enhances the density of states at the Fermi level and the effective electron-phonon coupling constant for low-energy phonon modes, which is the key to the understanding of high-temperature superconductivity.
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