Marginally Self-Averaging One-Dimensional Localization in Bilayer Graphene.

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 ln g with the varying chemical potential, in strongly insulating bilayer graphene (BLG), decay nearly logarithmically for a channel length up to L/xi approximate to 20, where xi is the localization length. This "marginal" self-averaging, and the corresponding dependence of < ln g > on L, suggests that transport in strongly gapped BLG occurs along strictly one-dimensional channels, where xi approximate to 0.5 +/- 0.1 mu m 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.