We have studied an infinite Hubbard chain with a spin-orbit coupling term, submitted to a uniform magnetic field as well as local phonons. By means of a Lang-Firsov transformation, we show that an effective interacting fermion model emerges. Moreover, a self-consistent mean-field theory of this model,
formulated in terms of thermal Green's functions,
shows that a BCS term emerges, thus leading to a superconducting phase transition at zero temperature. We find analytical expressions for the phase boundary, that agree well with exact numerical diagonalization of the Hamiltonian.
Enrique Munoz, Edson Vernek, and Victor Apel, "Phonon-induced superconductivity in a self-consistent Hubbard model (Conference Presentation)," Proc. SPIE 10357, Spintronics X, 103571L (Presented at SPIE Nanoscience + Engineering: August 08, 2017; Published: 11 October 2017); https://doi.org/10.1117/12.2276951.5606333762001.
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