Topological valley currents via ballistic edge modes in graphene superlattices near the primary Dirac point

Graphene on hexagonal boron nitride (hBN) can exhibit a topological phase via mutual crystallographic alignment. Recent measurements of nonlocal resistance ($R_{nl}$) near the secondary Dirac point (SDP) in ballistic graphene/hBN superlattices have been interpreted as arising due to the quantum valley Hall state. We report hBN/graphene/hBN superlattices in which $R_{nl}$ at SDP is negligible, but below 60 K approaches the value of $h\mathrm{/}2e^2$ in zero magnetic field at the primary Dirac point with a characteristic decay length of 2 $\mu$m. Furthermore, nonlocal transport transmission probabilities based on the Landauer-B"uttiker formalism show evidence for spin-degenerate ballistic valley-helical edge modes, which are key for the development of valleytronics