Quasi-classical dynamics of current carriers in graphene

After a general introduction to the physics of massless Dirac fermions in graphene and their exotic properties (first of all, chiral or Kleinian tunneling, that is, passing through arbitrarily high and wide potential barriers), I will present a quasi-classical theory of these phenomena. For the case of a one-dimensional potential barrier, a homogeneous asymptotic approximation can be developed, which gives a very accurate analytical solution for an arbitrary barrier shape [1,2]. Then, I will move on to the discussion of electronic optics in graphene, namely, the theory of Veselago electronic lenses, including consideration of wave front catastrophes [3,4]. I will also briefly consider the general theory of the propagation of Dirac fermions in a two-dimensional potential relief [5], as a special case of the quasi-classical approximation for matrix Hamiltonians. Finally, I will briefly describe the features of chiral tunneling for the case of two-layer graphene [6].
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