Conductance through disordered graphene nanoribbons: Standard and anomalous electron localization

Abstract

Conductance fluctuations produced by the presence of disorder in zigzag and armchair graphene nanoribbons are studied. We show that quantum transport in zigzag nanoribbons takes place via edge states which are exponentially localized, as in the standard Anderson localization problem, whereas for armchair nanoribbons the symmetry of the graphene sublattices produces anomalous localization, or delocalization. We show that these two different electron localizations lead to significant differences of the conductance statistics between zigzag and armchair nanoribbons. In particular, armchair nanoribbons show nonconventional large conductance fluctuations relative to those of Anderson-localized electrons. We calculate analytically the complete distribution of conductances for both types of ribbons. Without free fitting parameters, we verify our theoretical results by performing numerical simulations of disordered zigzag and armchair nanoribbons of experimentally achievable lengths and widths.

6 pages, 3 figures, Minor changes

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• A Lloyd-model generalization: Conductance fluctuations in one-dimensional disordered systems
• Delay time of waves performing Lévy walks in 1D random media
• Wave transmission and its universal fluctuations in one-dimensional systems with Lévy-like disorder: Schrödinger, Klein-Gordon and Dirac equations
• Transition between anomalous and Anderson localization in systems with non-diagonal disorder driven by time-periodic fields
• Statistics of coherent waves inside media with Lévy disorder
• Four-terminal voltage fluctuations in disordered graphene nanoribbons: Anderson and anomalous localization effects
• Characterizing random 1D media with an embedded reflector via scattered waves