The Dirac point and linear band structure in graphene bestow it with remarkable electronic and optical properties, a subject of intense ongoing research. Explanations of high electronic mobility in graphene often invoke the masslessness of electrons based on the effective relativistic Dirac-equation behavior, which are inaccessible to most undergraduate students and are not intuitive for non-physics researchers unfamiliar with relativity. Here, we show how to use only basic concepts from semiconductor theory and the linear band structure of graphene to explain its unusual effective mass and mobility, and compare them with conventional metals and semiconductors. We discuss the more intuitive concept of transverse effective mass, which emerges naturally from these basic derivations, and which approaches zero in the limit of undoped graphene at low temperature and is responsible for its extremely high mobility.
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April 2019
April 01 2019
Electron mobility in graphene without invoking the Dirac equation
Chaitanya K. Ullal;
Chaitanya K. Ullal
Department of Materials Science and Engineering, Rensselaer Polytechnic Institute
, 110 8th Street, Troy, New York 12180
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Jian Shi;
Jian Shi
Department of Materials Science and Engineering, Rensselaer Polytechnic Institute
, 110 8th Street, Troy, New York 12180
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Ravishankar Sundararaman
Ravishankar Sundararaman
a)
Department of Materials Science and Engineering, Rensselaer Polytechnic Institute
, 110 8th Street, Troy, New York 12180
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a)
Electronic mail: sundar@rpi.edu
Am. J. Phys. 87, 291–295 (2019)
Article history
Received:
July 01 2018
Accepted:
February 10 2019
Citation
Chaitanya K. Ullal, Jian Shi, Ravishankar Sundararaman; Electron mobility in graphene without invoking the Dirac equation. Am. J. Phys. 1 April 2019; 87 (4): 291–295. https://doi.org/10.1119/1.5092453
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