Electron–Lattice Coupling in Armchair Graphene Nanoribbons

Abstract

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.

Spin-Orbit Effects on the Dynamical Properties of Polarons in Graphene Nanoribbons

“…Importantly, it was demonstrated that – besides the difference in the charge localization – for AGNR belonging to 3p + 2 family the electronic charge is symmetrically displaced throughout all the ribbon’s length regardless of considering SO coupling or not. These findings agree with both theoretical and experimental results recently reported in literature 17,18,28 . Regarding the polaron dynamics, it was obtained that the electric field and the dynamic process itself do not destabilize the carrier in the presence of a SO coupling term.…”

“…23 . The parameters adopted here for the model Hamiltonian were successfully employed in other works presenting a good track-record 23–28 : t 0  = 2.7 eV, M is the carbon core’s mass, K  = 21 eV/Å 2 , α  = 4.1 eV/Å, and a  = 1.44 Å.…”

Impurity effects on polaron dynamics in graphene nanoribbons

“…3 -i.e. extended along the GNR length -were recently discussed in detail in a previous work [22]. On the other hand, the charge localization in the presence of impurities in GNRs (as shown in Fig.…”

“…where f/ l;i ðnÞg and fe l g are the eigenfunctions and eigenvalues of the Hamiltonian at a given time t [20]. Here, we have adopted the following values for the parameters: t 0 ¼ 2:7 eV [21][22][23], K = 57 eV/Å 2 [21], and a ¼ 7:6 eV=Å [24]. According to the literature, these values for t 0 and K are the most convenient to accurately reproduce the electronic structure features of graphene lattice.…”

Electron-Phonon Coupling in Silicene Nanoribbons

“…Then, one can use this new set of coordinates as input to the eigenvalue problem. The procedure is repeated until the achieving a given convergence criteria [1,2]. Spin-orbit coupling effects are introduced in order to treat the systems more accurately.…”