2006
DOI: 10.1103/physrevb.73.235411
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Electronic states of graphene nanoribbons studied with the Dirac equation

Abstract: We study the electronic states of narrow graphene ribbons ("nanoribbons") with zigzag and armchair edges. The finite width of these systems breaks the spectrum into an infinite set of bands, which we demonstrate can be quantitatively understood using the Dirac equation with appropriate boundary conditions. For the zigzag nanoribbon we demonstrate that the boundary condition allows a particle-and a hole-like band with evanescent wavefunctions confined to the surfaces, which continuously turn into the well-known… Show more

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Cited by 1,321 publications
(720 citation statements)
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“…Graphene is a gapless semiconductor [65], but when structuring the graphene into a nanometer-sized ribbon, its properties change depending on the edge profiles. Theoretical studies show that an armchair ribbon will be semiconducting [66][67][68][69] and that a zigzag-edged ribbon is metallic with a current profile that peaks at the edges [66,[69][70][71]. Both armchair and zigzag nanoribbons have been proposed to present promising platforms for DNA sequencing in a large number of theoretical reports [72][73][74][75][76][77][78][79], and experimentalists have begun to explore this approach [80][81][82][83][84][85].…”
Section: Inplane Transport Of a Graphene Nanoribbon With A Nanoporementioning
confidence: 99%
“…Graphene is a gapless semiconductor [65], but when structuring the graphene into a nanometer-sized ribbon, its properties change depending on the edge profiles. Theoretical studies show that an armchair ribbon will be semiconducting [66][67][68][69] and that a zigzag-edged ribbon is metallic with a current profile that peaks at the edges [66,[69][70][71]. Both armchair and zigzag nanoribbons have been proposed to present promising platforms for DNA sequencing in a large number of theoretical reports [72][73][74][75][76][77][78][79], and experimentalists have begun to explore this approach [80][81][82][83][84][85].…”
Section: Inplane Transport Of a Graphene Nanoribbon With A Nanoporementioning
confidence: 99%
“…Zigzag-edged nanoribbons can carry a spin current and, hence, can be used in spin-based nanoelectronic systems [9]. Armchair-edged nanoribbons show either metallic or semiconducting behavior as their width changes [6]. In addition, graphene nanoislands, such as triangular islands with well-defined zigzag edges, can show magnetic properties [10,11].…”
Section: Introductionmentioning
confidence: 99%
“…[51][52][53] For example, it is known that mechanical straining can alter the band gaps of graphene nanoribbons significantly. [51,[54][55][56][57][58][59] Similarly, it has also been shown that straining can change the band gaps for h-BN nanoribbons [15,18] and large area h-BN. [60] We note that in reference, [60] the authors investigated the bandgap as a function of strain to the strain where the bandgap eventually approaches zero.…”
mentioning
confidence: 99%