  Topological phonon states in crystalline materials have attracted significant
research interests due to their importance for fundamental physical phenomena,
yet their implication on phonon thermal transport remains largely unexplored.
Here, we use density functional theory calculations and symmetry analyses to
explore topological phonon phase transitions under uniaxial strains and their
tuning effects on thermal transport in titanium monoxide (TiO). Our calculation
shows that application of 10% tension significantly diminishes lattice thermal
conductivity of TiO by 77% and 66% along the a and c axes, respectively, at
room temperature. This suppression is found to result largely from the breaking
of symmetry protected degeneracy of acoustic branches, which induces a
substantial enhancement of phonon scattering phase space due to the easier
fulfillment of scattering selection rules. Our study provides evidence for the
importance of phononic band topology in modulating thermal conductivity and
offers a promising route towards controlling solid-state heat transport.
