We report the effects of electron-lattice coupling on the charge density distribution study of armchair graphene nanoribbons (GNRs). Here, we perform a theoretical investigation explaining the unexpected electronic density states observed experimentally. By means of a tight-binding approach with electron-lattice coupling, we obtained the same characteristic pattern of charge density along the C-C bonds suggested by both scanning tunneling and transmission electron microscopic measurements. Our results suggest electronic localized states whose sizes are dependent on the GNR width. We also show that our model rescues the quasi-particle charge-transport mechanism in GNRs. The remarkable agreement with experimental evidence allows us to conclude that our model could be, in many aspects, a fundamental tool when it comes to the phenomenological understanding of the charge behavior in this kind of system.

The field-induced dynamics of polarons in armchair graphene nanoribbons (GNRs) is theoretically investigated in the framework of a two-dimensional tight-binding model with lattice relaxation. Our findings show that the semiconductor behavior, fundamental to polaron transport to take place, depends upon of a suitable balance between the GNR width and the electron-phonon (e-ph) coupling strength. In a similar way, we found that the parameter space for which the polaron is dynamically stable is limited to an even narrower region of the GNR width and the e-ph coupling strength. Interestingly, the interplay between the external electric field and the e-ph coupling plays the role to define a phase transition from subsonic to supersonic velocities for polarons in GNRs.

By means of a 2-D tight-binding model with lattice relaxation in a first-order expansion, we report different polaron properties depending on the armchair graphene nanoribbons width family as well as on its size. We find that representatives of the 3p+2 family do not present a polaronic-mediated charge transport. As for 3p and 3p+1 families, the polaron behavior was completely dependent on the system's width. In particular, we observed a greater degree of delocalization for broader nanoribbons; narrower nanoribbons of both families, on the contrary, typically presented a more localized polaronic-type transport. Energy levels and occupation numbers analysis are performed to rigorously assess the nature of the charge carrier. Time evolution in the scope of the Ehrenfest molecular dynamics was also carried out to confirm the collective behavior and stability of the carrier as a function of time. We were able to determine that polarons in nanoribbons of 3p family present higher mobility than those in 3p+1 nanoribbons. These results identify the transport process that takes place for each system, and they allow the prediction of the mobility of the charge carriers as a function of the structural properties of the system, thus providing guidance on how to improve the efficiency of graphene nanoribbon-based devices.