  Nothing is known about the thermal conductivity in twisted bilayer graphene
(TBG) at small twist angles, and how it approaches its aligned value as the
twist angle approaches 0 degrees. To provide insight into these questions, we
perform large scale non-equilibrium molecular dynamics calculations on
commensurate TBG structures with angles down to 1.87 degrees. The results show
a smooth, non-monotonic behavior of the thermal conductivity with respect to
the commensurate lattice constant. As the commensurate lattice constant
increases, the thermal conductivity initially decreases by 50%, and then it
returns 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 elastic
constant, the wrinkling intensity, and the out-of-plane ZA2 phonon frequency.
The picture that emerges of the physical mechanism governing the thermal
conductivity is that misorientation reduces the shear elastic constant; the
reduced shear elastic constant enables greater wrinkling; and the greater
wrinkling reduces the thermal conductivity. The small-angle behavior of the
thermal conductivity raises the question of how do response functions approach
their aligned values as the twist angle approaches 0 degrees. Is the approach
gradual, discontinuous, or a combination of the two?
