Fractal butterflies of Dirac fermions in monolayer and bilayer graphene

• Published in: IET circuits, devices & systems Vol. 9; no. 1; pp. 19 - 29
• Main Authors: Chakraborty, Tapash, Apalkov, Vadym M
• Format: Journal Article
• Language: English
• Published: Stevenage The Institution of Engineering and Technology 01.01.2015; John Wiley & Sons, Inc
• Subjects: bilayer graphene; Bilayers; Bloch electrons; Butterflies; Butterflies & moths; butterfly spectrum; Dirac fermions; Dynamical systems; Dynamics; Electron energy; electron-electron interaction; electronic properties; Energy; Energy spectra; Fermions; Fractal analysis; fractal butterflies; Fractals; Graphene; Hofstadter butterfly; Magnetic fields; Magnetic properties; magnetoconductance probe; magnetoresistance; Moire patterns; Moiré pattern; monolayer graphene; Monolayers; perpendicular magnetic field; semiconductor nanostructures; semiconductor systems; Semiconductors; single-electron energy spectrum; Special Issue on Graphene Electronics; magnetoresistance; monolayer graphene; Hofstadter butterfly; Bloch electrons; monolayers; electronic properties; bilayer graphene; fractal butterflies; magnetoconductance probe; single-electron energy spectrum; graphene; perpendicular magnetic field; Dirac fermions; Moiré pattern; electron-electron interaction; semiconductor systems; semiconductor nanostructures; butterfly spectrum
• DOI: 10.1049/iet-cds.2014.0275
• ISSN: 1751-858X; 1751-8598

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.