GRAPHENE SYNTHESIS CHARACTERIZATION PROPERTIES

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GRAPHENE SYNTHESIS CHARACTERIZATION PROPERTIES ( graphene-synthesis-characterization-properties )

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CoompmlexpWleKBxAWpprKoxBimaAtiopnspinrGorxapimhenaetEiloecntrosn-iHnoleGWraavepguhidesnien MEaglnectictrFoielnd -Hole Waveguides in Magnetic Field 85 we obtain the classical trajectories connecting x(0) and x. For electrons and holes one should seek solution to the Dirac system zero-order problem in the form with unknown amplitude σ(0)(x). Solvability of the problem ψ0 = σ(0)(x)e1 (5) (H − EI)ψ1 = −Rψ0, E = h1,2, requires that the orthogonality condition with complex conjugation must hold < e1, R(σ(0)(x)e1) >= 0, Using the basic elements of the techniques in (15), from the orthogonality condition one should obtain the transport equation for σ(0)(x) dσ(0) 1 (0) (0) de1 dt +2σ logJ+σ =0, (6) where is the geometrical spreading with respect to the hamiltonian system with h1,2 = U ± vF p. It J(t,γ)= ∂(x1,x2) ∂(t, γ) has a solution (0) c0 −iθ/2 = √J e σ , c0 = const. For upper order terms, one should seek solution in the form where σ(j) may be found straight forward 2 (H − EI)ψj = −Rψj−1, ψj = σ(j)e1 + σ(j)e2, (7) 12 σ(j) = . 2 2(E − U(x)) Then, from the orthogonality condition, one should obtain (j) 1 −iθ/2 σ1 =√Je < e1, R(σ(j)e1 + σ(j)e2) >= 0, 12 t cj− e 0 iθ/2 (j) Jdt , cj=const.

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