  Layering two-dimensional van der Waals materials provides unprecedented
control over atomic placement, which could enable tailoring of vibrational
spectra and heat flow at the sub-nanometer scale. Here, using
spatially-resolved ultrafast thermoreflectance and spectroscopy, we uncover the
design rules governing cross-plane heat transport in superlattices assembled
from monolayers of graphene (G) and MoS2 (M). Using a combinatorial
experimental approach, we probe nine different stacking sequences: G, GG, MG,
GGG, GMG, GGMG, GMGG, GMMG, GMGMG and identify the effects of vibrational
mismatch, interlayer adhesion, and junction asymmetry on thermal transport.
Pure G sequences display signatures of quasi-ballistic transport, whereas
adding even a single M layer strongly disrupts heat conduction. The
experimental data are described well by molecular dynamics simulations which
include thermal expansion, accounting for the effect of finite temperature on
the interlayer spacing. The simulations show that a change of only 1.5% in the
layer separation can lead to a nearly 100% increase of the thermal resistance.
Using these design rules, we experimentally demonstrate a 5-layer GMGMG
superlattice with an ultralow effective cross-plane thermal conductivity
comparable to air, paving the way for a new class of thermal metamaterials with
extreme properties.
