  A solid conducts heat through both transverse and longitudinal acoustic
phonons, but a liquid employs only longitudinal vibrations. Here, we report
that the crystalline solid AgCrSe2 has liquid-like thermal conduction. In this
compound, Ag atoms exhibit a dynamic duality that they are exclusively involved
in intense low-lying transverse acoustic phonons while they also undergo local
fluctuations inherent in an order-to-disorder transition occurring at 450 K. As
a consequence of this extreme disorder-phonon coupling, transverse acoustic
phonons become damped as approaching the transition temperature, above which
they are not defined anymore because their lifetime is shorter than the
relaxation time of local fluctuations. Nevertheless, the damped longitudinal
acoustic phonon survives for thermal transport. This microscopic insight might
reshape the fundamental idea on thermal transport properties of matter and
facilitates the optimization of thermoelectrics.
