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2 φ (ρ,z ) =0 for the electrical potential φ (ρ,z ) in cylindrical coordinates. The solution of the Poisson equation in all the N+1 regions can be written as φ(ρ,z) =exp (iqρ ) [αexp (qz ) + βexp (-qz )] and depends on a total of 2 (N+1 ) constants. Two are fixed by imposing boundary conditions φ (ρ,z→±) =0 at infinity. The remaining 2N constants are fixed by the continuity of the potential φ across each layer and by imposing that the electric displacement has a discontinuity. Let D= be the electric displacement above the th layer and Iμ be the dielectric constant in this region of space (E=-z φ ). Then one has to impose that D+1 - D=4π σfor =N,...,1, where σ=-e is the Fourier transform of -e δ2 (ρ) δ [z- (-1 ) d ]
-
2 φ (ρ,z ) =0 for the electrical potential φ (ρ,z ) in cylindrical coordinates. The solution of the Poisson equation in all the N+1 regions can be written as φ(ρ,z ) =exp (iqρ ) [ αexp (qz ) + βexp (-qz ) ] and depends on a total of 2 (N+1 ) constants. Two are fixed by imposing boundary conditions φ (ρ,z→±) =0 at infinity. The remaining 2N constants are fixed by the continuity of the potential φ across each layer and by imposing that the electric displacement has a discontinuity. Let D= be the electric displacement above the th layer and Iμ be the dielectric constant in this region of space (E=-z φ ). Then one has to impose that D+1 - D=4π σfor =N,...,1, where σ=-e is the Fourier transform of -e δ2 (ρ) δ [z- (-1 ) d ].
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10.1103/PhysRevLett.98.216801;
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E. G. Mishchenko, Phys. Rev. Lett. 98, 216801 (2007) 10.1103/PhysRevLett. 98.216801
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10.1103/PhysRevB.78.115426
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M. Polini, A. Tomadin, R. Asgari, and A. H. MacDonald, Phys. Rev. B 78, 115426 (2008). 10.1103/PhysRevB.78.115426
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(2008)
Phys. Rev. B
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Polini, M.1
Tomadin, A.2
Asgari, R.3
MacDonald, A.H.4
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