  The Anderson localization of thermal phonons has been shown only in few
nano-structures with strong random disorder by the exponential decay of
transmission to zero and a thermal conductivity maximum when increasing 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.
