Lattice thermal conductivity of graphene nanoribbons: Anisotropy and edge roughness scattering

We present a calculation of the thermal conductivity of graphene nanoribbons (GNRs), based on solving the Boltzmann transport equation with the full phonon dispersions, a momentum-dependent model for edge roughness scattering, as well as three-phonon and isotope scattering. The interplay between edge roughness scattering and the anisotropy of the phonon dispersions results in thermal conduction that depends on the chiral angle of the nanoribbon. Lowest thermal conductivity occurs in the armchair direction and highest in zig-zag nanoribbons. Both the thermal conductivity and the degree of armchair/zig-zag anisotropy depend strongly on the width of the nanoribbon and the rms height of the edge roughness, with the smallest and most anisotropic thermal conductivities occurring in narrow GNRs with rough edges.