Phase transition of polarons in bilayer graphene nanoribbons

Stacking graphene nanoribbons (GNRs) is the natural path to obtain semiconductors with exotic quantum phenomena by manipulating the interlayer coupling. Recently, a report demonstrated that, during charge transport, interlayer coupling significantly affects the phonon breathing modes. Therefore, a reliable physical description of charged carriers must explicitly address the coupling nature of the electronic and lattice phenomena. In this work, we gauge the influence of interlayer coupling (t (& BOTTOM;)) on the formation of charged carriers in a bilayer of an armchair graphene nanoribbon using a model Hamiltonian with electron-phonon coupling. We find different quasiparticle solutions depending on the t (& BOTTOM;) magnitude. As it increases, the carrier's charge progressively delocalizes along the layers, resulting in two interlayer polaron morphologies: the non-symmetric (0 meV <t (& BOTTOM;) & LE; 45 meV) and the symmetric (t (& BOTTOM;)> 45 meV). These solutions also manifest in the band structure through first-order electronic phase transitions in the intragap states with a significant energy shift of about 0.3 eV. Consequently, the carrier's mobility and effective mass are expected to be highly sensitive to t (& BOTTOM;), suggesting that mechanical stress can regulate the mechanism. The findings extend to other GNR bilayers, potentially inspiring the development of novel nanoelectronics based on highly confined stacked systems.