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Low-dimensional phonon transport effects in ultra-narrow, disordered graphene nanoribbons

We investigate the influence of low-dimensionality and disorder in phonon transport in ultra-narrow armchair graphene nanoribbons (GNRs) using non-equilibrium Greens function (NEGF) simulation techniques. We specifically focus on how different parts of the phonon spectrum are influenced by geometrical confinement and line edge roughness. With the introduction of line edge roughness, the phonon transmission is reduced, but non-uniformly throughout the spectrum. We identify four distinct behaviors within the phonon spectrum in the presence of disorder: i) the low-energy, low-wavevector acoustic branches have very long mean-free-paths and are affected the least by edge disorder, even in the case of ultra-narrow W=1nm 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) quasi-acoustic 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 especially as the channel length increases; 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=3nm, under moderate roughness, both the low-energy acoustic modes and dense regions of optical modes can retain semi-ballistic transport properties, even for channel lengths up to L=1 um. Modes in the sparse regions of the spectrum fall into the localization regime even for channel lengths as short as 10s of nanometers.