  We introduce a technique to calculate thermal conductivity in disordered
nanostructures: a finite-difference time-domain (FDTD) solution of the elastic
wave equation combined with the Green-Kubo formula. The technique captures
phonon wave behavior and scales well to nanostructures that are too large or
too surface disordered to simulate with many other techniques. We investigate
the role of Rayleigh waves and surface disorder on thermal transport by
studying graphenelike nanoribbons with free edges (allowing Rayleigh waves) and
fixed edges (prohibiting Rayleigh waves). We find that free edges result in a
significantly lower thermal conductivity than fixed ones. Free edges both
introduce Rayleigh waves and cause all low-frequency modes (bulk and surface)
to become more localized. Increasing surface disorder on free edges draws
energy away from the center of the ribbon and toward the disordered edges,
where it gets trapped in localized surface modes. These effects are not seen in
ribbons with fixed boundary conditions and illustrate the importance of phonon
surface modes in nanostructures.
