Influence of phonon-phonon coupling on superconducting state in honeycomb-type crystal lattice

We have taken into account the superconducting state inducing in the crystal lattice of the honeycomb-type. In the framework of the Eliashberg theory, we have determined the thermodynamic properties of the system. The phonon spectral function, which is the input parameter in the Eliashberg equations, has been calculated by using the thermodynamic Green functions. We have considered the model of the coupled Einstein oscillators with frequency ω₀ = 100 meV. We have shown that the increasing inter-phonon coupling constant (f) causes the rapid growth of the critical temperature ([T_C]max = 36.2 K) just below the maximum value of f equal to 0.25ω₀. Simultaneously, the order parameter and the thermodynamic critical field take the values increasingly distant from the predictions of the BCS theory, which results from the strong-coupling and the retardation effects.