Origin of nonlocal resistance in multiterminal graphene on hexagonal-boron-nitride: Fermi surface edge currents rather than Fermi sea topological valley currents

摘要: The recent observation [R. V. Gorbachev et al., Science {\bf 346}, 448 (2014)] of nonlocal resistance $R_\mathrm{NL}$ near the Dirac point (DP) multiterminal graphene on aligned hexagonal boron nitride (G/hBN) has been interpreted as consequence topological valley Hall currents carried by Fermi sea states just beneath bulk gap $E_g$ induced inversion symmetry breaking. However, conductivity $\sigma^v_{xy}$, quantized inside $E_g$, is not directly measurable. Conversely, Landauer-B\"{u}ttiker formula, numerically exact approach to observable transport quantities, yields $R_\mathrm{NL} \equiv 0$ for same simplistic Hamiltonian gapped that generates $\sigma^v_{xy} \neq 0$. We combine ab initio with quantum calculations demonstrate G/hBN wires zigzag edges host dispersive edge DP are absent in theories based Hamiltonian. Although such exist also isolated wires, hBN required modify their energy-momentum dispersion and generate persisting presence disorder. Concurrently, resolve long-standing puzzle why highly insulating state rarely observed. conclude observed unrelated conjectured spectra.