Figure 1

Electron energy dispersion of a graphene nanostrip (solid bands). This particular nanostrip has a width of $N_{zz}=50$ interior zigzag lines, which corresponds to approximately $11\mathrm{nm}$. The dispersion is compared to that of a (25,25) carbon nanotube (dashed bands). Due to the edge states, there is only one channel close to the Fermi level which is located at $E=0$.Reuse & Permissions

Figure 2

First Brillouin zone with (a) quantized electronic bands and (b) phonon branches satisfying $q_x=0$. Phonons at the $K$-point can scatter an electron in state $K$ into state $K^{\prime }$.Reuse & Permissions

Figure 3

Lattice vibrations which cause non-negligible intraband electron-phonon coupling. The two modes represent (a) a LA phonon and (b) a TO phonon at a $K$-point. Note that due to the LA and LO degeneracy, the LA mode has been obtained in the limit $q\to (4∕3)(\pi ∕a)$.Reuse & Permissions

Figure 4

Effects due to a frozen TO phonon in a GNS $(N_{zz}=50)$ lattice. (a) The electron dispersion of the nanostrip is calculated with the frozen phonon at the $K$-point (solid bands) and is compared to that with no frozen phonon (dashed bands). Due to the frozen phonon, there are gaps at $k=0$, which reflect an electron-phonon coupling between $k=-(2∕3)(\pi ∕a)$ and $k^{\prime }=(2∕3)(\pi ∕a)$. (b) The same calculation with the frozen phonon at the $\Gamma$-point. This phonon has a coupling which causes forward scattering. (c) The energy difference between the electron dispersions with and without the frozen phonon at the $\Gamma$-point. The energy difference in the nanostrip (solid curve) is compared to that of a (25,25) armchair nanotube (dashed curve). At low electron wave vectors, the energy differences are similar, while at high wave vectors, the energy difference in the nanostrip is suppressed by its edge states.Reuse & Permissions

Figure 5

(a) Scattering rates of a $N_{zz}=50$ zigzag-edge GNS at $300\mathrm{K}$ as a function of electron energy. The LA and TO phonons cause intraband scattering and the LO phonon interband scattering. Intraband phonon absorption occurs at all electron energies, while intraband phonon emission requires energies larger than the threshold energy for the particular branch. The threshold energies are about 0.16 and $0.18\mathrm{eV}$ for the LA and TO branches, respectively. (b) The total mean free path at room temperature due to electron-phonon scattering. The mean free path increases with the chemical potential since a higher chemical potential reduces the number of unoccupied electron states.Reuse & Permissions