  Fundamental understanding of thermal transport in compounds with ultra-low
thermal conductivity remains challenging, primarily due to the limitations of
conventional lattice dynamics and heat transport models. In this study, we
investigate the thermal transport in quasi-one-dimensional (1D) copper halide
CsCu2I3 by employing a combination of first principles-based self-consistent
phonon calculations and a dual-channel thermal transport model. Our results
show that the 0-K unstable soft modes, primarily dominated by Cs and I atoms in
CsCu2I3, can be an-harmonically stabilized at ~ 75 K. Furthermore, we predict
an ultra-low thermal conductivity of 0.362 Wm^(-1) K^(-1) along the chain axis
and 0.201 Wm^(-1) K^(-1) along cross chain direction in CsCu2I3 at 300 K.
Importantly, we find that an unexpected anomalous trend of increasing
cross-chain thermal conductivity with increasing temperature for CsCu2I3,
following a temperature dependence of ~T 0.106, which is atypical for a single
crystal and classified as an abnormal glass-like behavior. The peculiar
temperature-dependent behavior of thermal conductivity is elucidated by the
dominant wave-like tunnelling of phonons in thermal transport of CsCu2I3 along
cross-chain direction. In contrast, particle-like phonon propagation primarily
contributes to the chain-axis thermal conductivity across the entire
temperature range of 300-700 K. The sharp difference in the dominant thermal
transport channels between the two crystallographic directions can be
attributed to the unique chain-like quasi-1D structure of CsCu2I3. Our study
not only illustrates the microscopic mechanisms of thermal transport in CsCu2I3
but also paves the way for searching for and designing materials with ultra-low
thermal conductivity.
