Four-terminal voltage fluctuations in disordered graphene nanoribbons: Anderson and anomalous localization effects

The voltage is a sensitive quantity to quantum interference in coherent electronic transport. We study the voltage fluctuations in disordered graphene nanoribbons with zigzag and armchair edge terminations in a four-terminal configuration. We show that the average and standard deviation of the voltage oscillates with the separation of the attached voltage probes and depend on the coupling strength of the probes. The voltage fluctuations can be large enough to observe negative voltages for weakly coupled probes. As we numerically verified, the voltage fluctuations are described within a random matrix approach for weakly disordered nanoribbons at energies away from the Fermi energy. However, near the Fermi energy, zigzag nanoribbons exhibit Anderson localization, whereas electrons are anomalously localized in armchair nanoribbons. This distinction leads to different voltage statistics for zigzag and armchair nanoribbons.