Hạn chế và Độ đồng nhất Điện tử trong Graphene Epitaxial Có Mẫu
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#Graphene epitaxial mỏng #silicon carbide #graphit hóa chân không #vận chuyển điện tử #hạn chế lượng tử #độ đồng nhất phaTài liệu tham khảo
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The momentum is with reference to the K point in graphene i.e. E = v 0 ħ | k – k ( K )| where k is the wave vector.
Carbon nanotubes are a specific example of confined graphene where the momentum perpendicular to the axis is quantized according to k perp = n / D where D is the diameter.
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Equation 1 is obtained by applying the interpolation scheme of ( 27 ) to Dirac electrons. Applying the Schrödinger equation H |ψ 〉 = E |ψ 〉 twice gives H eff |ψ 〉 = E eff |ψ 〉 with H eff = H 2 and E eff = E 2 . It can be shown that H eff = H 2 describes free-like electrons close to the band edges (either from the Dirac equation or the tight-binding model; the origin of energies is taken at the band edges). Using the square root interpolation formula of ( 27 ) applied to H eff = H 2 gives \batchmode \documentclass[fleqn 10pt legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \(\mathbf{\mathit{E}}_{n}=\sqrt{\mathbf{\mathit{E}}_{\mathrm{eff}_{n}}}\) \end{document} for the energies at the bottom of band n .
N. M. R. Peres A. H. Castro Neto F. Guinea arxiv.org/abs/cond-mat/0603771 (2006).
We follow the convention of indexing the MR peaks ( 24 25 ) rather than the valleys.
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N. M. R. Peres F. Guinea A. H. Castro Neto arxiv.org/abs/cond-mat/0512091 (2005).
Supported by NSF grant 0404084 U.S. Department of Energy grant DE-FG02-02ER45956 a grant from Intel Research Corporation and a USA-France travel grant from CNRS. We acknowledge discussions with J. D. Meindl and help from the staff of the Georgia Tech MIRC clean room. Any opinions findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the research sponsors.