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We have developed an efficient order-N real-space Kubo approach for thecalculation of the phonon conductivity which outperforms state-of-the-artalternative implementations based on the Green's function formalism. The methodtreats efficiently the time-dependent propagation of phonon wave packets inreal space, and this dynamics is related to the calculation of the thermalconductance. Without loss of generality, we validate the accuracy of the methodby comparing the calculated phonon mean free paths in disordered carbonnanotubes (isotope impurities) with other approaches, and further illustrateits upscalability by exploring the thermal conductance features in large widthedge-disordered graphene nanoribbons (up to ~20 nm), which is out of the reachof more conventional techniques. We show that edge-disorder is the mostimportant scattering mechanism for phonons in graphene nanoribbons withrealistic sizes and thermal conductance can be reduced by a factor of ~10.

Phonon transport in large scale carbon-based disordered materials: Implementation of an efficient order-N and real-space Kubo methodology