  Topological insulators realized in materials with strong spin-orbit
interactions challenged the long-held view that electronic materials are
classified as either conductors or insulators. The emergence of controlled,
two-dimensional moire patterns has opened new vistas in the topological
materials landscape. Here we report on evidence, obtained by combining
thermodynamic measurements, local and non-local transport measurements, and
theoretical calculations, that robust topologically non-trivial, valley Chern
insulators occur at charge neutrality in twisted double-bilayer graphene
(TDBG). These time reversal-conserving valley Chern insulators are enabled by
valley-number conservation, a symmetry that emerges from the moir\'e pattern.
The thermodynamic gap extracted from chemical potential measurements proves
that TDBG is a bulk insulator under transverse electric field, while transport
measurements confirm the existence of conducting edge states. A
Landauer-Buttiker analysis of measurements on multi-terminal samples allows us
to quantitatively assess edge state scattering and demonstrate that it does not
destroy the edge states, leaving the bulk-boundary correspondence largely
intact.
