Strong-Coupling Superconductivity with D-Wave Order Parameter and S-Wave Gap

Abstract

Over the last decade a few competing models of high-temperature superconductivity were proposed, most of them with short-range interactions due to electron repulsive correlations. However, assessing the role of different interactions in novel superconductors one has to take into account that these materials are highly polarizable ionic lattices, where the Fröhlich electron-phonon interaction with optical phonons should be strong. Indeed, a parameter-free estimate[1] based on the measured dielectric constants shows that the polaron binding energy, E_p is about 0.5 eV or larger in oxides. Hence, the Fröhlich interaction should play an important role. Also, because of a poor screening, the direct unscreened Coulomb repulsion is important. There are extensive experimental [2, 3, 4, 5, 6, 7] and theoretical studies[8, 9, 10, 11], which prove that the electron-phonon (el-ph) interaction in high-T_c superconductors is exceptionally strong. Electron correlations are strong as well shaping the Mott-Hubbard insulating state of many parent (undoped) compounds [12]. Hence, the theory of high- T_c superconductors must treat both interactions on equal footing as was suggested some time ago [8]. Motivated by the fact that el-ph interaction is long-ranged in the cuprates because of poor screening, we have proposed a new approach to the high-T_c problem introducing a finite-range (Fröhlich) interaction [13, 14, 15]. The analytical [13] and Monte-Carlo [15] studies of a simple chain model with a long-range el-ph coupling revealed a several order lower effective mass of the small Fröhlich polaron compared with the small Holstein polaron. Later the single-polaron and bipolaron cases of the chain model were analyzed in more detail in Refs.[16] and [17], respectively. These