Edge scattering of electrons in graphene: Boltzmann equation approach to the transport in graphene nanoribbons and nanodisks

We discuss the contribution of edge scattering to the conductance of graphene nanoribbons and nanoflakes. Using different possible types of the boundary conditions for the electron wave function at the edge, we found dependences of the momentum relaxation time and conductance on the geometric sizes and on the carrier density. We also consider the case of ballistic nanoribbon and nanodisk, for which the edge scattering is the main mechanism of momentum relaxation.

Figure 1

Conductivity as a function of $L$ for different values of $k_F$ (Berry-Mondragon boundary conditions at the edges). For numerical calculations we take ${\gamma }_{\text{BM}}={10}^2(a_0/\ell )\left(k_F{a}_0\right)$.

Figure 2

Conductivity as a function of $L$ for different values of $k_F$ (zigzag boundary conditions at the edges). Here we take ${\gamma }_z={10}^8(a_0/\ell ){\left(k_F{a}_0\right)}^5$.

Figure 3

Relaxation time as a function of $k_y/k_F$ for different values of the parameter $\xi =a^2{k}_F^2$ (Berry-Mondragon boundary conditions at the edges).

Figure 4

Relaxation time as a function of $k_y/k_F$ for different values of the parameter $\xi$ (zigzag boundary conditions at the edges).