Deciphering the origin of nonlocal resistance in multiterminal graphene on hexagonal-boron-nitride with ab initio quantum transport: Fermi surface edge currents rather than Fermi sea topological valley currents

J M Marmolejo-Tejada,S Roche,P Plecháč,P-H Chang,B K Nikolić,J H García,M D Petrović,X-L Sheng,A Cresti

doi:10.1088/2515-7639/aad585

Abstract

The recent observation (Gorbachev et al 2014 Science 346 448) of nonlocal resistance RNL near the Dirac point (DP) of multiterminal graphene on aligned hexagonal-boron nitride (G/hBN) has been interpreted as the consequence of topological valley Hall currents carried by the Fermi sea states just beneath the bulk gap Eg induced by inversion symmetry breaking. However, the corresponding valley Hall conductivity , quantized inside Eg, is not directly measurable. Conversely, the Landauer–Büttiker formula, as a numerically exact approach to observable nonlocal transport quantities, yields RNL ≡ 0 for the same simplistic Hamiltonian of gapped graphene that generates via the Kubo formula. We combine ab initio with quantum transport calculations to demonstrate that G/hBN wires with zigzag edges host dispersive edge states near the DP that are absent in theories based on the simplistic Hamiltonian. Although such edge states exist also in isolated zigzag graphene wires, aligned hBN is required to modify their energy–momentum dispersion and generate near the DP. The Fermi surface-determined edge currents carrying the nonlocal signal persist also in the presence of edge disorder and over long distances. Concurrently, they resolve the long-standing puzzle of why the highly insulating state of G/hBN is rarely observed. Thus, we conclude that the observed RNL is unrelated to Fermi sea topological valley currents conjectured for gapped Dirac spectra.

Highlights

The physics of graphene on hBN with their crystallographic axes aligned is expected to be governed by the broken spatial inversion symmetry due to different potentials on two triangular sublattices of carbon atoms induced by the hBN substrate
VNL and RNL directly and has been used for decades to model nonlocal transport measurements [23, 24], yields RNL ≡ 0 near the Dirac point (DP) in figure 2(c) in multiterminal geometries whose channel length is larger than its width (L/W ; 4 in the experiments of [1])
We combine Wannier tight-binding Hamiltonian (TBH) with the Kubo formula in figure 4(b), where we find quantized svxy in the gap

Summary

Introduction

The physics of graphene on hBN with their crystallographic axes aligned is expected to be governed by the broken spatial inversion symmetry due to different potentials on two triangular sublattices of carbon atoms induced by the hBN substrate. The latter conclusion is reproduced in figure A1(f) in appendix A where we compute the band structure of a G/hBN wire with zigzag edges using the same simplistic Hamiltonian employed in prior theoretical studies [1,2,3,4, 15, 19, 32].

Results

Conclusion