Aharonov-Bohm effect and giant magnetoresistance in graphene nanoribbon
  rings

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Abstract

We report a numerical study on Aharonov-Bohm (AB) effect and giant magnetoresistance in rectangular rings made of graphene nanoribbons (GNRs). We show that in low energy regime where only the first subband of contact GNRs contributes to the transport, the transmission probability can be strongly modulated, i.e., almost fully suppressed, when tuning a perpendicular magnetic field. On this basis, strong AB oscillations with giant negative magnetoresistance can be achieved at room temperature. The magnetoresistance reaches thousands % in perfect GNR rings and a few hundred % with edge disordered GNRs. The design rules to observe such strong effects are also discussed. Our study hence provides guidelines for further investigations of the AB interference and to obtain high magnetoresistance in graphene devices.

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The electronic properties of graphene

K. S. Novoselov, A. K. Geim, A. H. Castro Neto … (2007)

This article reviews the basic theoretical aspects of graphene, a one atom thick allotrope of carbon, with unusual two-dimensional Dirac-like electronic excitations. The Dirac electrons can be controlled by application of external electric and magnetic fields, or by altering sample geometry and/or topology. We show that the Dirac electrons behave in unusual ways in tunneling, confinement, and integer quantum Hall effect. We discuss the electronic properties of graphene stacks and show that they vary with stacking order and number of layers. Edge (surface) states in graphene are strongly dependent on the edge termination (zigzag or armchair) and affect the physical properties of nanoribbons. We also discuss how different types of disorder modify the Dirac equation leading to unusual spectroscopic and transport properties. The effects of electron-electron and electron-phonon interactions in single layer and multilayer graphene are also presented.

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Quantum Spin Hall Effect in Graphene

E. Mele, C. L. Kane (2004)

We study the effects of spin orbit interactions on the low energy electronic structure of a single plane of graphene. We find that in an experimentally accessible low temperature regime the symmetry allowed spin orbit potential converts graphene from an ideal two dimensional semimetallic state to a quantum spin Hall insulator. This novel electronic state of matter is gapped in the bulk and supports the quantized transport of spin and charge in gapless edge states that propagate at the sample boundaries. The edge states are non chiral, but they are insensitive to disorder because their directionality is correlated with spin. The spin and charge conductances in these edge states are calculated and the effects of temperature, chemical potential, Rashba coupling, disorder and symmetry breaking fields are discussed.

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Energy Gaps in Graphene Nanoribbons

Marvin L. Cohen, Young-Woo Son, Steven Louie (2007)

Based on a first-principles approach, we present scaling rules for the band gaps of graphene nanoribbons (GNRs) as a function of their widths. The GNRs considered have either armchair or zigzag shaped edges on both sides with hydrogen passivation. Both varieties of ribbons are shown to have band gaps. This differs from the results of simple tight-binding calculations or solutions of the Dirac's equation based on them. Our {\it ab initio} calculations show that the origin of energy gaps for GNRs with armchair shaped edges arises from both quantum confinement and the crucial effect of the edges. For GNRs with zigzag shaped edges, gaps appear because of a staggered sublattice potential on the hexagonal lattice due to edge magnetization. The rich gap structure for ribbons with armchair shaped edges is further obtained analytically including edge effects. These results reproduce our {\it ab initio} calculation results very well.