Anisotropy of lattice thermal conductivity in edge-disordered graphene nanoribbons

We present a calculation of the thermal conductivity of graphene nanoribbons, based on solving the Boltzmann transport equation with the full phonon dispersions, a momentum-dependent model for boundary scattering, as well as three-phonon and isotope scattering. The interplay between strong edge roughness scattering and the anisotropy of the phonon dispersions results in thermal conduction that strongly depends on the chiral angle of the nanoribbon. A minimum occurs in the armchair direction and a maximum is attained in zig-zag nanoribbons. We also show that both the thermal conductivity and the amount 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 occuring in narrow GNRs with rough edges.