Marginally Self-Averaging One-Dimensional Localization in Bilayer Graphene

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.