Communications in Mathematical Physics

, Volume 367, Issue 3, pp 941–989 | Cite as

Magnetic Oscillations in a Model of Graphene

  • Simon Becker
  • Maciej ZworskiEmail author


We consider a quantum graph as a model of graphene in constant magnetic field and describe the density of states in terms of relativistic Landau levels satisfying a Bohr–Sommerfeld quantization condition. That provides semiclassical corrections (with the magnetic flux as the semiclassical parameter) in the study of magnetic oscillations.


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We gratefully acknowledge support by the UK Engineering and Physical Sciences Research Council (EPSRC) Grant EP/L016516/1 for the University of Cambridge Centre for Doctoral Training, the Cambridge Centre for Analysis (SB), by the National Science Foundation under the Grant DMS-1500852 and by the Simons Foundation (MZ).We would also like to thank Nicolas Burq for useful discussions, Semyon Dyatlov for help with MATLAB coding and insightful comments and Hari Manoharan for introducing us to molecular graphene and for allowing us to use Figs. 1 and 7(b).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.DAMTPUniversity of CambridgeCambridgeUK
  2. 2.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

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