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

Abstract

We have developed an efficient order-$N$ real-space Kubo approach for the calculation of the phonon conductivity which outperforms state-of-the-art alternative implementations based on the Green's function formalism. The method treats efficiently the time-dependent propagation of phonon wave packets in real space, and this dynamics is related to the calculation of the thermal conductance. Without loss of generality, we validate the accuracy of the method by comparing the calculated phonon mean free paths in disordered carbon nanotubes (isotope impurities) with other approaches, and further illustrate its upscalability by exploring the thermal conductance features in large width edge-disordered graphene nanoribbons (up to $\ensuremath{\sim}20\text{ }\text{nm}$), which is out of the reach of more conventional techniques. We show that edge disorder is the most important scattering mechanism for phonons in graphene nanoribbons with realistic sizes and thermal conductance can be reduced by a factor of $\ensuremath{\sim}10$.