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2 results

  • 3 - Quantum transport via evanescent waves

  • Mikhail I. Katsnelson, Radboud Universiteit Nijmegen
  • Book:
    The Physics of Graphene
    Published online:
    24 May 2020
    Print publication:
    19 March 2020, pp 63-76

  • Summary

    The chapter explains a physics of minimal conductivity in graphene. It is shown that a new type of electronic transport arises in graphene, namely, electron tunneling via zero modes of Dirac operator. The relation to Zitterbewegung concept of relativistic quantum mechanics is demonstrated. We calculate the value of minuimal conductivity and shot noise in the neutrality point, and consider Aharonov–Bohm effect in undoped graphene rings.

  • 5 - Edges, nanoribbons, and quantum dots

  • Mikhail I. Katsnelson, Radboud Universiteit Nijmegen
  • Book:
    The Physics of Graphene
    Published online:
    24 May 2020
    Print publication:
    19 March 2020, pp 108-140

  • Summary

    Boundary conditions for electron wave functions in graphene are discussed, both in Dirac approximation and for the honeycomb lattice. We start with the model of "neutrino billiard." Then, we discuss typicality of zigzag boundary conditions for the terminated honeycomb lattice, existence of zero-energy edge mode for these conditions, electronic states and conductance quantization in graphene nanoribbons, level statistics for graphene quantum dots, explanation of quantum Hall effects in terms of topologically protected edge modes, and Aharonov–Bohm effect in multiconnected graphene flakes. The latter case is used as an example of the general topological concept of spectral flow.