A model for energy spectrum of superlattice on the base of graphene placed on the striped dielectric substrate is proposed. A direct current component which appears in that structure perpendicularly to pulling electric field under the influence of elliptically polarized electromagnetic wave was derived. A transverse current density dependence on pulling field magnitude and on magnitude of component of elliptically polarized wave directed along the axis of a superlattice is analyzed.
We solve the Dirac equation, which describes charge massless chiral relativistic carriers in a twodimensional graphene. We have identified and analysed a novel pseudospin-dependent scattering effect. We compute the tunneling conductance and generalize the analytical result in the presence of the tunable atomic potential of a graphene strip. The absence of back scattering in graphene is shown to be due to Berry's phase which corresponds to a sign change of the wave function under a spin rotation of a particle. We use the transfer matrix approach and find that the electric conductance of doped graphene increases due to atomic potential fluctuations.
The possibility of the existence of soliton solutions of the generalized sine-Gordon equation (also referred to as Kryuchkov-Kukhar equation (KKeq)) has been investigated numerically. This equation describes the propagation of electromagnetic waves in a graphene superlattice. The computational errors associated with the implicit form of the expression defining the kink solution of the considering equation are estimated. The differences between the forms before and after the collision of pulses, propagating towards each other, are estimated. On the basis of the obtained results it is concluded that the considered kink solution is not a soliton.
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