Cooper pair distribution function of misaligned graphene sheets and determination of superconducting properties

Abstract

We report a novel determination of the Copper-pair distribution function Dcp(ω,Tc) involving vibrational energy (ω) and critical temperature (Tc). This distribution establishes energy vibrational interval where the Cooper pairs arise. Based on experimental superconductivity for a bilayer graphene twisted at small angles of 1.05° and 1.16° and critical temperatures of 1.7 K and 0.5 K respectively, recently reported elsewhere, we estimated Dcp(ω,Tc) for the same graphene configuration by calculating the Eliashberg function, electronic density and the vibrational density from ab initio calculations. The phonon fingerprint distribution with energy between 0.0 meV and 0.6 meV contributes to the superconductivity, while the Eliashberg functions show a correlation with the critical temperature in this interval. Based on the Functional Derivative Method (FDM), critical temperatures of 1.7 K (1.05°) and 1.71 K (1.16°) are found. Since no experimental data for intermediate angles has been reported, the critical temperature for 1.10° was determined around 1.68 K. The theoretical reason why all computed critical temperatures are very similar is that the Eliashberg function profile has minor changes for the three angles in all the spectral range, and therefore the critical temperatures have minor changes.