Edges states and anomalous Aharonov-Bohm-type oscillation in anti-dot lattice graphenes formed by nanoporous alumina template mask

Edge states of graphene with a zigzag structure theoretically have extremely high electronic density of states (EDOS), electron localization, and polarized spin transport as well [1]. However, few studies have reported on the experimental observation of edge states and related quantum phenomena. Here, we report on the nonlithographic and low-damage fabrication of honeycomb-like nanopore arrays (anti-dot lattice) on thin multilayered graphenes utilizing nanoporous alumina template masks [2]. We confirm the presence of high EDOS at the edges of the nanopores using STM observation. We find periodic magnetoresistance oscillations with two different periods over a wide magnetic field range (anomalous Aharonov-Bohm-type effect [3]) (e.g., high fields at where the diameter of cyclotron-motion electrons is smaller than diameter of the nanopore). These findings clearly suggest the presence of localized electrons and edge states at the nanopore edges of graphene. \\[4pt] [1] K. Nakada, G. Dresselhaus, M. S. Dresselhaus et al., Phys. Rev. B 54, 17954 (1996). \\[0pt] [2]T. Shimizu, J. Haruyama et al., To be published on Phys. Rev. Lett. \\[0pt] [3] D. Weiss, K.von Klitzing et al., Phys. Rev. Lett. 70, 4118 (1993).