Signatures of non-adiabatic superconductivity in lithium-decorated graphene

Recent experimental studies confirmed that a long searched conventional superconducting phase in graphene can be induced via lithium deposition. However, the canonical character of the lithium-decorated graphene (LiC$_{6}$) superconductor postulated therein, as defined by the Bardeen-Cooper-Schrieffer (BCS) theory, is ambiguous due to the moderate electron-phonon coupling constant and low Fermi energy in this material. Herein, this issue is addressed within the Migdal-Eliashberg formalism and beyond it via the first-order electron-phonon vertex corrections, to account for the potentially pivotal effects, hitherto not captured. The conducted analysis yields similar value of the metal-superconductor transition temperature as in the previous studies ($T_{C} \sim 6$ K), yet for a weaker depairing electron correlations, which magnitude in the non-adiabatic regime approaches predictions of the Morel-Anderson model. Moreover, the characteristic ratio of the pairing gap and the inverse temperature is found to notably exceeds estimates of the BCS theory. In a results, it is argued that the superconducting state in LiC$_{6}$ may have non-canonical character strongly influenced by the non-adiabatic and retardation effects. Moreover, discussed phase appears as a vital case study, which suggests that other two-dimensional superconductors of hexagonal structure may exhibit similar non-canonical behavior as LiC$_{6}$.