Superconducting energy gap and Critical Temperature of Cuprates from the Multilayer Boson-Fermion Formalism

High temperature superconductors (HTSC) which present a cuasi-2D multilayer structure, such as cuprates, are not completely described by the BCS theory. Here we use the Boson-Fermion (BF) [1] formalism adjusted to incorporate multilayers [2] to calculate the properties of cuprates as a mixture composed by electrons as fermions and electron Cooper pairs (CP) as composite bosons. The multilayers are generated by applying a Dirac Comb Potential in the orthogonal direction with respect to the layers, thus the bosons and fermions satisfied the Kronig-Penney relation [3]. In X-Y planes, bosons have a linear energy-momentum relation [4] given by ε(K) = 2 E_F,2 - Δ₀ + c K_ρ, where E_F,2 is the Fermi energy in 2D, Δ₀ the energy gap and c a constant, while the electrons have the energy ε(k) = ħ²k²/2m_e, with m_e the electron mass. With the energy spectrum of the BF mixture we are able to calculate the energy gap, critical temperature and chemical potential, as functions of the plane impenetrability P and the separation a among them, by solving simultaneously the energy gap-like equation and the number equation. We compare our results with experimental cuprate data.

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