  Understanding the phonon behavior in semiconductors from a topological
physics perspective provides more opportunities to uncover extraordinary
physics related to phonon transport and electron-phonon interactions. While
various kinds of topological phonons have been reported in different
crystalline solids, their microscopic origin has not been quantitatively
uncovered. In this work, four typical analytical interatomic force constant
(IFC) models are employed for wurtzite GaN and AlN to help establish the
relationships between phonon topology and real-space IFCs. In particular,
various nearest neighbor IFCs, i.e., different levels of nonlocality, and IFC
strength controlled by characteristic coefficients, can be achieved in these
models. The results demonstrate that changes in the strength of both the IFCs
and nonlocal interactions can induce phonon phase transitions in GaN and AlN,
leading to the disappearance of existing Weyl phonons and the appearance of new
Weyl phonons. These new Weyl phonons are the result of a band reversal and have
a Chern number of 1. Most of them are located in the kz=0 plane in pairs, while
some of them are inside or at the boundary of the irreducible Brillouin zone.
Among the various Weyl points observed, certain ones remain identical in both
materials, while others exhibit variability depending on the particular case.
Compared to the strength of the IFC, nonlocal interactions show much more
significant effects in inducing the topological phonon phase transition,
especially in cases modeled by the IFC model and SW potential. The larger
number of 3NN atoms provides more space for variations in the topological
phonon phase of wurtzite AlN than in GaN, resulting in a greater abundance of
changes in AlN.
