Low-dimensional phonon transport effects in ultranarrow disordered graphene nanoribbons

We investigate the influence of low dimensionality and disorder in phonon transport in ultranarrow armchair graphene nanoribbons (GNRs) using nonequilibrium Green's function (NEGF) simulation techniques. We specifically focus on how different parts of the phonon spectrum are influenced by geometrical confinement and line edge roughness. Under ballistic conditions, phonons throughout the entire phonon energy spectrum contribute to thermal transport. With the introduction of line edge roughness, the phonon transmission is reduced, but in a manner which is significantly nonuniform throughout the spectrum. We identify four distinct behaviors within the phonon spectrum in the presence of disorder: (i) the low-energy, low-wave vector acoustic branches have very long mean-free paths and are affected the least by edge disorder, even in the case of ultranarrow W = 1 nm wide GNRs; (ii) energy regions that consist of a dense population of relatively "flat" phonon modes (including the optical branches) are also not significantly affected, except in the case of the ultranarrow W = 1nm GNRs, in which case the transmission is reduced because of band mismatch along the phonon transport path; (iii) "quasiacoustic" bands that lie within the intermediate region of the spectrum are strongly affected by disorder as this part of the spectrum is depleted of propagating phonon modes upon both confinement and disorder [resulting in sparse E(q) phononic band structure], especially as the channel length increases; and (iv) the strongest reduction in phonon transmission is observed in energy regions that are composed of a small density of phonon modes, in which case roughness can introduce transport gaps that greatly increase with channel length. We show that in GNRs of widths as small as W = 3 nm, under moderate roughness, both the low-energy acoustic modes and dense regions of optical modes can retain semiballistic transport properties, even for channel lengths up to L = 1 mu m. These modes tend to completely dominate thermal transport. Modes in the sparse regions of the spectrum, however, tend to fall into the localization regime, even for channel lengths as short as tens of nanometers, despite their relatively high phonon group velocities.