The combination of a field-tunable band gap, 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 lng with the varying chemical potential, in strongly insulating bilayer graphene (BLG), decay nearly logarithmically for a channel length up to L/ξ≈20, where ξ is the localization length. This "marginal" self-averaging, and the corresponding dependence of ⟨lng⟩ on L, suggests that transport in strongly gapped BLG occurs along strictly one-dimensional channels, where ξ≈0.5±0.1 μm was found to be much longer than that expected from the bulk band gap. Our experiment reveals a nontrivial localization mechanism in gapped BLG, governed by transport along robust edge modes.
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