Electron-phonon coupling in Kekul\'{e}-ordered graphene

Abstract

Breaking the intrinsic chirality of quasiparticles in graphene enables the emergence of new and intriguing phases. One such paradigmatic example is the bond density wave, which leads to a Kekul\'{e}-ordered structure and underpins exotic electronic states where electron-phonon interactions can play a fundamental role. Here, it is shown that the relevant physics of these correlations can be resolved locally, according to the behavior of interatomic characteristics. For this purpose a robust distance-dependent framework for describing electronic structure of graphene with Kekul\'{e} bond order is presented. Given this insight, the strength of electron-phonon interactions is found to scale linearly with the electronic coupling, contributing to a uniform picture of this relationship in distorted graphene structures. Moreover, it is shown that the introduced distortion yields a strongly non-uniform spatial distribution of the pairing strength that eventually leads to the induction of periodically distributed domains of enhanced electron-phonon coupling. These findings help elucidate certain peculiar aspects of phonon-mediated phenomena in graphene, particularly the associated superconducting phase, and offer potential pathways for their further engineering.