Superconductivity in a Hubbard-Fröhlich model and in cuprates

Abstract

Using the variational Monte Carlo method, we find that a relatively weak long-range electron-phonon interaction induces a d-wave superconducting state in doped Mott-Hubbard insulators and/or strongly correlated metals with a condensation energy significantly larger than can be obtained with Coulomb repulsion only. Moreover, the superconductivity is shown to exist for infinite on-site Coulomb repulsion without the need for additional mechanisms such as spin fluctuations to mediate d-wave superconductivity. We argue that our superconducting state is robust with respect to a more intricate choice of the trial-wave function and that a possible origin of high-temperature superconductivity lies in a proper combination of strong electron-electron correlations with poorly screened Fröhlich electron-phonon interaction.

Variational Monte Carlo method for electron-phonon coupled systems

“…However, most of its applications are restricted to systems without the electronphonon coupling or effective electron models in the antiadiabatic limit [38]. The main reason for this may be the difficulty of constructing a suitable and tractable variational wave functions with a small number of variational parameters for such systems.…”

Unconventional High-Temperature Superconductivity from Repulsive Interactions: Theoretical Constraints

“…According to the recent numerical studies, unconventional pairing from the strong Coulomb repulsion is not possible either, since the corresponding condensation energy, if any, is several times lower than the condensation energy caused by a realistic electron-phonon interaction. For instance, the maximum condensation energy gain with the repulsive Hubbard interaction U ¼ 8 is at least 3 times lower than that caused by a rather weak electron-phonon interaction with ¼ 0:075 in strongly correlated electron systems near optimum doping [12].…”

Effect of Electron-Phonon Interaction Range for a Half-Filled Band in One Dimension

“…The second term represents the electron-phonon interaction, in the form of a nonlocal density-displacement coupling, with the density operatorn i = σn iσ andn iσ = c † iσ c iσ . The matrix elements are chosen as [9,10,27] …”