access icon free Fractal butterflies of Dirac fermions in monolayer and bilayer graphene

© The Institution of Engineering and Technology
Received 02/09/2014, Accepted 13/10/2014, Revised 02/10/2014, Published 27/01/2015

Bloch electrons in a perpendicular magnetic field exhibit unusual dynamics that has been studied for more than half a century. The single-electron energy spectrum of this system, the Hofstadter butterfly has been the subject of theoretical and experimental investigations for the past two decades. Experimental observation of these unusual spectra in semiconductor nanostructures, however, met with only limited success. The fractal nature of the butterfly spectrum was finally observed in 2013, thanks to the unique electronic properties of graphene. Here, the authors present an overview of the theoretical understanding of Hofstadter butterflies in monolayer and bilayer graphene. First, they briefly discuss the energy spectra in conventional semiconductor systems. The electronic properties of monolayer and bilayer graphene are then presented. Theoretical background on the Moiré pattern in graphene and its application in the magnetoconductance probe that resulted in graphene butterflies are explained. They have also touched upon the important role of electron–electron interaction in the butterfly pattern in graphene. Experimental efforts to investigate this aspect of fractal butterflies have just begun. They conclude by discussing the future prospects of butterfly search, especially for interacting Dirac fermions in graphene.

Inspec keywords: graphene; monolayers; magnetoresistance

Other keywords: Moiré pattern; bilayer graphene; electronic properties; single-electron energy spectrum; Bloch electrons; Dirac fermions; electron-electron interaction; semiconductor systems; Hofstadter butterfly; perpendicular magnetic field; semiconductor nanostructures; butterfly spectrum; magnetoconductance probe; monolayer graphene; fractal butterflies

Subjects: Galvanomagnetic and other magnetotransport effects (semiconductors/insulators); Electronic structure of fullerenes and fullerene-related materials; intercalation compounds; Electrical properties of graphene and graphene-related materials (thin films, low-dimensional and nanoscale structures)

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