Marginally Self-Averaging One-Dimensional Localization in Bilayer Graphene

Abstract

The combination of field tunable bandgap, topological edge states, and valleys in the band structure, makes insulating bilayer graphene a unique localized system, where the scaling laws of dimensionless conductance g remain largely unexplored. Here we show that the relative fluctuations in ln g with the varying chemical potential, in strongly insulating bilayer graphene (BLG) decay nearly logarithmically for channel length up to L/$\xi$ $\approx$ 20, where $\xi$ is the localization length. This 'marginal' self averaging, and the corresponding dependence of <ln g> on L, suggest that transport in strongly gapped BLG occurs along strictly one-dimensional channels, where $\xi$ $\approx$ 0.5$\pm$0.1 $\mu$m was found to be much longer than that expected from the bulk bandgap. Our experiment reveals a nontrivial localization mechanism in gapped BLG, governed by transport along robust edge modes.

arXiv commentThis document is the Author's version of a submitted work that was subsequently accepted for publication in Physical Review Letters

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• Emergent inhomogeneity and non-locality in a graphene field-effect transistor on a near-parallel moire superlattice of transition metal dichalcogenides
• Mechanism of Universal Conductance Fluctuations
• Scattering theory of transport through disordered magnets
• Spectral analysis of universal conductance fluctuations