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CoompmlexpWleKBxAWpprKoxBimaAtiopnspinrGorxapimhenaetEiloecntrosn-iHnoleGWraavepguhidesnien MEaglnectictrFoielnd -Hole Waveguides in Magnetic Field 89 i (S0(s)+S1(s)n) +∞ j/2 = e h ̄ ∑ h ̄ ψ j ( s , ν ) , j=0 where S0(s) and S1(s) were chosen as in (18), (19) S0(s) = a(s) + α (x(0)γ1 + x(0)γ2) ds, 212 S1(s) = α (x(0)γ1 − x(0)γ2), 221 a(s)= E−U0(s), vF where U(x) = U0(s) + U1(s)n + U2(s)n2 + ..., γi(s), i = 1, 2 are the cartesian components of en(s). Thus, for unknown ψj(s, ν) we obtain a recurrent system (H0−EI)ψ0 =0, (H0−EI)ψ1 =−vFH1ψ0, (H0−EI)ψ2 =−vFH1ψ1−vFH2ψ0,... with operators H0, H1, H2, ... ⎛ (0)) vF((γ2 +iγ1)S ̇0 +(γ1 −iγ2)S ̇1 − αx2 (0)) 2 (0)) ⎞ H0 = ⎝ U0 vF((γ2 −iγ1)S ̇0 +(γ1 +iγ2)S ̇1 − αx2 +iαx1 ) 2 ⎠ −iαx1 ) U0 (0)) 22 U0 (γ2+iγ1)(E−U0) = (γ2−iγ1)(E−U0) U0 , (U1 − U0−E)ν −e−iθ(∂ν +αν) H=vρ, 1 F eiθ(∂ν −αν) (U1 − U0−E)ν ρ (U2−U1)ν2 e−iθ(ν∂ν+αν2 −i∂s) ρ ρ 2ρ H2=vF H=⎝ ρ eiθ(−ν∂ν+αν2 −i∂s) (U2−U1)ν2 , ρ2ρ ρ ⎛⎞ (Uj − Uj−1 )νj 0 j 0 (U−Uj−1)νj ⎠, j>2, jρ where eiθ = γ2 − iγ1, ρ(s) is the radius of curvature of the classical trajectory, and S ̇0 means a derivative with respect to s. Solving the zero-order problem (H0 − EI)ψ0 = 0, we come to the eigen-vector problem H0eα=hαeα, α=1,2, hα =U0±vF|a(s)|, 11 11 e1 = √2 eiθ , e2 = √2 −eiθ If E > U0, then E = h1, if E < U0, then E = h2. .PDF Image | GRAPHENE SYNTHESIS CHARACTERIZATION PROPERTIES
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