Achieving the ultimate lower limit of thermal conductivity is essential for advancing thermal management, thermoelectric energy conversion, and phononic engineering. Here, we integrate Bayesian optimization with machine-learning-potential molecular dynamics to discover stacking configurations in graphene/twisted-${\mathrm{MoS}}_2$ $(\mathrm{Gra}/\mathrm{T}\text{−}{\mathrm{MoS}}_2)$ heterostructures that exhibit an exceptionally low crossplane thermal conductivity of $0.006\mathrm{W}{\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$, which is 3–4 times lower than that of typical ultralow-thermal-conductivity porous materials $(0.02–0.04\mathrm{W}{\mathrm{m}}^{-1}{\mathrm{K}}^{-1})$, surpassing the conventional lower bound of thermal conductivity in solid materials. Phonon transmission and spectral analyses reveal that this extreme thermal insulation originates not merely from phonon localization but from the overdamped regime of phonon dynamics, where strong interlayer asymmetry and disorder suppress the restoring forces that sustain oscillatory motion. In this regime, phonons lose their quasiparticle nature, and heat conduction transitions from propagating vibrations to localized energy dissipation. This work introduces phonon overdamping as a physical mechanism governing the ultimate limit of lattice thermal conductivity and establishes a data-driven framework for designing next-generation materials with tunable and ultralow heat transport.

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• Heat transfer
• Phonons
• Thermal conductivity
• Thermal properties
• 2-dimensional systems
• Graphene
• Transition metal dichalcogenides
• Twisted heterostructures
• Bayesian methods
• First-principles calculations
• Molecular dynamics