Supplementary information files for: Anomalous thermal conductivity enhancement in low dimensional resonant nanostructures due to imperfections

Nanophononic metamaterials have broad applications in fields such as heat management, thermoelectric energy conversion, and nanoelectronics. Phonon resonance in pillared low-dimensional structures has been suggested to be a feasible approach to reduce thermal conductivity (TC). In this work, we study the effects of imperfections in pillared nanostructures based on graphene nanoribbons (GNR), using classical molecular dynamics simulations and harmonic lattice dynamics. The TC of perfect pillared GNR is only about 13% of that of pristine GNR due to the strong phonon resonant hybridization in pillared GNR. However, introducing imperfections such as vacancy defects and mass mismatch between the pillars and the base material, and alloy disorder in the pillars, can weaken the resonant hybridization and abnormally increase the TC. We show that both vacancy defects and mass mismatch can reduce the penetration of the resonant modes from the pillars into the base material, while the alloy disorder in the pillars can scatter the phonons inside them, which turns regular resonance into a random one with weaker hybridization. Our work provides useful insight into the phonon resonance mechanisms in experimentally relevant low dimensional nanostructures containing various imperfections.