  Recently, the twist-angle effect on 2D van der Walls (vdW) materials, such as
bilayer graphene, has attracted great attention. Many novel electronic,
magnetic and even optical properties induced by such effect have been
discovered. However, the twist-angle effect on phononic property is not so
remarkable. By investigating the thermal conductivity of twist bilayer graphene
(TBG), here we reveal that the trivial twist-angle effect on phononic property
observed in previous studies is owing to the non-localization nature of
phonons. This characteristic makes phonons hardly trapped by the weak
interlayer potentials induced by the twist-angle dependent Moir\'e pattern. We
propose that the twist-angle effect can be effectively enhanced by increasing
the interface coupling. In use of a sandwich structure composed of h-BN and
TBG, we demonstrate that the thermal conductivity of TBG can be either
significantly increased or dramatically decreased, under the synergistic
modulation of interlayer coupling strength and twist angle. Particularly, the
twist-angle effect can lead to a nontrivial reduction of thermal conductivity
up to 78% when a strong interlayer coupling is applied. The reduction is
several times larger than that observed in the freestanding TBG where the
reduction is attributed to the twist-angle dependent phonon scatterings induced
by the edge phonons. The underlying mechanism for the giant twist-angle
dependence of thermal conductivity is further revealed on the basis of phonon
transport theory. Our findings provide a platform for achieving efficient
twist-angle modulation on phonon transport property of vdW materials.
