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Nothing is known about the thermal conductivity in twisted bilayer graphene(TBG) at small twist angles, and how it approaches its aligned value as thetwist angle approaches 0 degrees. To provide insight into these questions, weperform large scale non-equilibrium molecular dynamics calculations oncommensurate TBG structures with angles down to 1.87 degrees. The results showa smooth, non-monotonic behavior of the thermal conductivity with respect tothe commensurate lattice constant. As the commensurate lattice constantincreases, the thermal conductivity initially decreases by 50%, and then itreturns to 90% of its aligned value as the angle is reduced to 1.89 degrees.These same qualitative trends are followed by the trends in the shear elasticconstant, the wrinkling intensity, and the out-of-plane ZA2 phonon frequency.The picture that emerges of the physical mechanism governing the thermalconductivity is that misorientation reduces the shear elastic constant; thereduced shear elastic constant enables greater wrinkling; and the greaterwrinkling reduces the thermal conductivity. The small-angle behavior of thethermal conductivity raises the question of how do response functions approachtheir aligned values as the twist angle approaches 0 degrees. Is the approachgradual, discontinuous, or a combination of the two?

Small Angle and Non-Monotonic Behavior of the Thermal Conductivity in Twisted Bilayer Graphene