  The electron-phonon interaction (EPI) is instrumental in a wide variety of
phenomena in solid-state physics, such as electrical resistivity in metals,
carrier mobility, optical transition and polaron effects in semiconductors,
lifetime of hot carriers, transition temperature in BCS superconductors, and
even spin relaxation in diamond nitrogen-vacancy centers for quantum
information processing. However, due to the weak EPI strength, most phenomena
have focused on electronic properties rather than on phonon properties. One
prominent exception is the Kohn anomaly, where phonon softening can emerge when
the phonon wavevector nests the Fermi surface of metals. Here we report a new
class of Kohn anomaly in a topological Weyl semimetal (WSM), predicted by
field-theoretical calculations, and experimentally observed through inelastic
x-ray and neutron scattering on WSM tantalum phosphide (TaP). Compared to the
conventional Kohn anomaly, the Fermi surface in a WSM exhibits multiple
topological singularities of Weyl nodes, leading to a distinct nesting
condition with chiral selection, a power-law divergence, and non-negligible
dynamical effects. Our work brings the concept of Kohn anomaly into WSMs and
sheds light on elucidating the EPI mechanism in emergent topological materials.
