Critical temperature of the nonadiabatic superconducting state in mono- and bilayer systems

The electron-phonon interaction can induce the superconducting state in the low-dimensional mono- and bilayer systems. However, the calculated value of the temperature of the transition from the metallic to the superconducting state is greatly affected by the accuracy of the applied model. If taken into account, the vertex corrections to the electron-phonon interaction are usually of significant value due to the low Fermi level of such materials and were found to contribute to the reduction of the calculated value of the critical temperature of the transition. This fact weakens the prospects for the possibility of induction of the nonadiabatic superconducting state at the relatively high critical temperature since an increase either in the electron-phonon coupling constant or in the Debye frequency leads to the simultaneous increase in the corrected Migdal ratio, while influencing the critical temperature to a greater degree.