  Artificially engineered 2D materials offer unique physical properties for
thermal management, surpassing naturally occurring materials. Here, using van
der Waals epitaxy, we demonstrate the ability to engineer extremely insulating
ultra-thin thermal metamaterials based on crystalline lattice-mismatched
Bi2Se3/MoSe2 superlattices and graphene/PdSe2 heterostructures with exceptional
thermal resistances (70-202 m^2K/GW) and ultralow cross-plane thermal
conductivities (0.01-0.07 Wm^-1K^-1) at room temperature, comparable to those
of amorphous materials. Experimental data obtained using frequency-domain
thermoreflectance and low-frequency Raman spectroscopy, supported by
tight-binding phonon calculations, reveal the impact of lattice mismatch,
phonon-interface scattering, size effects, temperature and interface thermal
resistance on cross-plane heat dissipation, uncovering different thermal
transport regimes and the dominant role of long-wavelength phonons. Our
findings provide essential insights into emerging synthesis and thermal
characterization methods and valuable guidance for the development of
large-area heteroepitaxial van der Waals films of dissimilar materials with
tailored thermal transport characteristics.
