Emergence of thermal magic strain and magic angle in moiré bilayer graphene

Despite intense studies focused on graphene-based systems, several facets of their behaviour remain unexplored. One such aspect is the effect that some forms of mechanical deformation have on the thermal conductivity (TC) of a multilayer graphene. To address this aspect, we investigate the TC of bilayer graphene subjected to uniform biaxial strain and interlayer twist using non-equilibrium molecular dynamics methods (NEMD). A pronounced local minimum in TC is identified at a characteristic strain (S≈0.019) and twist angle (θ≈1.1 ∘), which we term the thermal magic strain and thermal magic angle, respectively. The persistence of these extrema under variations in temperature, interlayer distance and size confirms their intrinsic structural origin. In addition, these extrema arise from deformation-induced moiré superlattices, which generate spatially heterogeneous atomic stress and enhance phonon scattering. The competition between increasing scattering-site density and stress delocalization leads to a non-monotonic thermal response. Phonon density of states analysis further supports this mechanism and confirms the role of geometric mismatch in tuning heat transport. Our findings establish geometric modulation as an effective strategy for tuning lattice thermal transport and extend the concept of magic-strain physics to phonon-mediated heat conduction in two-dimensional materials.