  Dislocations can greatly enhance the figure of merit of thermoelectric
materials by prominently reducing thermal conductivity. However, the evolution
of phonon modes with different energies when they propagate through a single
dislocation is unknown. Here we perform non-equilibrium molecular dynamics
simulation to study phonon transport in PbTe crystal with dislocations by
excluding boundary scattering and strain coupling effect. The
frequency-dependent heat flux, phonon mode analysis, and frequency-dependent
phonon mean free paths (MFPs) are presented. The thermal conductivity of PbTe
with dislocation density on the order of 10^15m^-2 is decreased by 62%. We
provide solid evidence of strong localization of phonon modes in dislocation
sample. Moreover, by comparing the frequency-dependent phonon MFPs between
atomistic modeling and traditional theory, it is found that the conventional
theories are inadequate to describe the phonon behavior throughout the full
phonon spectrum, and large deviation to the well-known semi-classical
Matthiessen's rule is observed. These results provide insightful guidance for
the development of PbTe based thermoelectrics and shed light on new routes for
enhancing the performance of existing thermoelectrics by incorporating
dislocations.
