  Due to the long range interaction in lead telluride (PbTe), the transverse
optical (TO) phonon becomes soft around the Brillouin zone center. Previous
studies have postulated that this zone-center softening causes the low thermal
conductivity of PbTe through either enlarged phonon scattering phase space
and/or strengthened lattice anharmonicity. In this work, we reported an
extensive sensitivity analysis of the PbTe thermal conductivity to various
factors: range and magnitude of harmonic and anharmonic interatomic force
constants, and phonon wavevectors in the three-phonon scattering processes. The
analysis reveals that the softening by long range harmonic interaction itself
does not reduce thermal conductivity and it is the large magnitude of the
anharmonic (cubic) force constants that realizes low thermal conductivity,
however, not through the TO phonons around the zone center but dominantly
through the ones with larger wavevectors in the middle of Brillion zone. The
work clarifies that local band softening cannot be a direct finger print for
low thermal conductivity and the entire Brillion zone needs to be characterized
on exploring low thermal conductivity materials.
