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The recent observation [R. V. Gorbachev et al., Science {\bf 346}, 448(2014)] of nonlocal resistance $R_\mathrm{NL}$ near the Dirac point (DP) ofmultiterminal graphene on aligned hexagonal boron nitride (G/hBN) has beeninterpreted as the consequence of topological valley Hall currents carried bythe Fermi sea states just beneath the bulk gap $E_g$ induced by the inversionsymmetry breaking. However, the valley Hall conductivity $\sigma^v_{xy}$,quantized inside $E_g$, is not directly measurable. Conversely, theLandauer-B\"{u}ttiker formula, as numerically exact approach to observablenonlocal transport quantities, yields $R_\mathrm{NL} \equiv 0$ for the samesimplistic Hamiltonian of gapped graphene that generates $\sigma^v_{xy} \neq0$. We combine ab initio with quantum transport calculations to demonstratethat G/hBN wires with zigzag edges host dispersive edge states near the DP thatare absent in theories based on the simplistic Hamiltonian. Although such edgestates exist also in isolated zigzag graphene wires, aligned hBN is required tomodify their energy-momentum dispersion and generate $R_\mathrm{NL} \neq 0$near the DP persisting in the presence of edge disorder. Concurrently, the edgestates resolve the long-standing puzzle of why the highly insulating state ofG/hBN is rarely observed. We conclude that the observed $R_\mathrm{NL}$ isunrelated to Fermi sea topological valley currents conjectured for gapped Diracspectra.

jphys materials

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