The Cooper-Pair Distribution Function of Untwisted-Misaligned Bilayer Graphene

The Cooper-pair distribution function Dcp(ω,Tc) of Untwisted-Misaligned Bilayer Graphene (UMBLG) in the presence of an external electric field is calculated and analysed within the framework of first-principle calculations. A bilayer graphene structure is proposed using a structural geometric approximation, enabling the simulation of a structure rotated at a small angle, avoiding a supercell calculation. The Dcp(ω,Tc) function of UMBLG indicates the presence of the superconducting state for specific structural configurations, which is consistent with the superconductivity in Twisted Bilayer Graphene (TBLG) reported in the literature. The Dcp(ω,Tc) function of UMBLG suggests that Cooper-pairs are possible in the low-frequency vibration region. Furthermore, the structural geometric approximation allowed the evaluation of the effect of the electric field on the superconducting state of UMBLG and its superconducting critical temperature through the Ncp parameter.