Thermal conductivity minimum of graded superlattices due to phonon localization

Anderson localization of thermal phonons has been shown only in few nanostructures with strong random disorder by the exponential decay of transmission to zero and a thermal conductivity maximum when increasing the system length. In this work, we present a path to demonstrate the phonon localization with distinctive features in graded superlattices with short-range order and long-range disorder. A thermal conductivity minimum with system length appears due to the exponential decay of transmission to a non-zero constant, which is a feature of partial phonon localization caused by the moderate disorder. We provide clear evidence of localization through the combined analysis of the participation ratio, transmission, and real-space phonon number density distribution based on our quantum transport simulation. The present work would promote heat conduction engineering by localization via the wave nature of phonons.