Superconductivity in cuasi-1D crystals from the Boson-Fermion theory

From the Boson-Fermion (BF) theory [1-2] where electrons coexist with two-electron (2eCPs) and explicitly two-hole (2hCP) Cooper pairs, both as composite bosons, we solve three coupled equations numerically: the particle number equation, the gap-like equations for 2eCPs and for 2hCPs, from where we obtain the superconducting thermodynamic properties. For a cuasi-1D crystalline superconductor, where its ions are modeled as Dirac’s delta potentials equally spaced, coexisting with the gaseous mixture of bosons and fermions, we report among other thermodynamic properties, the energy gap, the critical temperature, and the specific heat. By comparison with the experimental data [3] we find that by introducing the ions explicitly, our results are better than in the case of the mixture without external potential. Surprisingly, we find that the energy gap and the critical temperature present a disproportionate maximum for optimal values of the intensity and separation of the deltas, showing a resonance-like state. We thank partial support from grant DGAPA-PAPIIT-UNAM IN114523.

[1] V.V. Tolmachev, Phys. Lett. A 266, 400 (2000); [2] M. de Llano & V.V. Tolmachev, Physica A 317, 546 (2003); [3] P. Garoche, et al., J. Physique Lettres 43, L-147 (1982)