Strong Optical-Optical Avoided Crossings Suppress Thermal Conductivity in Ga-Substituted TlInTe₂

In crystalline solids, avoided crossing between acoustic and optical phonons is widely recognized as an effective mechanism for suppressing lattice thermal conductivity ($\kappa_l$). However, the role of avoided crossings among optical phonons remains largely unexplored due to their weak contribution to heat transport. Here, using first-principles calculations combined with the linearized Wigner transport equation (LWTE), we demonstrate that optical-optical avoided crossings can effectively reduce ($\kappa_l$) in TlIn$_{0.5}$Ga$_{0.5}$Te$_2$. Pristine TlInTe$_2$ exhibits strong optical phonon-dominated heat transport, where optical phonons contribute nearly 63% of $\kappa_l$. The phonon dispersion of TlInTe$_2$ shows several crossing points in the optical region, which evolve into avoided crossings after 50% Ga substitution. Irreducible representation analysis reveals that the crossing phonon branches in TlInTe$_2$ belong to different symmetry representations, whereas the corresponding branches in TlIn$_{0.5}$Ga$_{0.5}$Te$_2$ possess the same symmetry representation, which enables phonon modes to couple and results in gap opening at the crossing points. These avoided crossings significantly suppress the optical phonon group velocity, thereby reducing the optical phonon contribution from 63% to 44% and lowering $\kappa_l$ from 0.568 to 0.482 Wm$^{-1}$K$^{-1}$ at 300 K. Mode-averaged transport analysis further confirms that the suppression of $\kappa_l$ is primarily governed by reduced phonon group velocity ($v_g$), while enhanced anharmonic scattering provides an additional secondary contribution. Our results establish symmetry-modified optical-optical avoided crossing as an effective route to suppress optical phonon transport and reduce $\kappa_l$ in systems where optical phonons significantly contribute to heat transport.