Geodesic
Resonance scattering across the superlattice barrier and the dimensional quantization
Nanosistemy: fizika, himiâ, matematika, Tome 7 (2016) no. 5, pp. 816-834.

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Carbon nano-cluster cathodes exhibit a low threshold electron emission, which is 2–3 orders lower than on metals and semiconductors. We confirm the effect by direct experiments with graphene structures. We are suggesting a model based on the interference electrons wave function in 3D-space charge region of carbon structure interface with vacuum. The low-threshold emission is explained, in frames of the model, by the resonance properties of the barrier formed on the interface. Also in the following topics: interpretation of recent experimental findings for saturation of the field emission; local spectral analysis of multidimensional periodic lattices: dispersion via DN-map; examples of iso-energetic surfaces associated with solvable models of periodic lattice; Lagrangian version of the operator extension algorithm; solvable models of selected one-body spectral problems; quantum dot attached to the node of a quantum graph; a solvable model of a discrete lattice and spectral structure of a 1D superlattice via analytic perturbation procedure.
Keywords: periodic interface, carbon cover, Weyl-Titchmarsh function, resonance, field emission, DN-map, periodic interface, carbon cover, Weyl-Titchmarsh function, resonance, field emission, DN-map. 
@article{NANO_2016_7_5_a3,
     author = {B. Pavlov and A. Yafyasov},
     title = {Resonance scattering across the superlattice barrier and the dimensional quantization},
     journal = {Nanosistemy: fizika, himi\^a, matematika},
     pages = {816--834},
     publisher = {mathdoc},
     volume = {7},
     number = {5},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/NANO_2016_7_5_a3/}
}
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B. Pavlov; A. Yafyasov. Resonance scattering across the superlattice barrier and the dimensional quantization. Nanosistemy: fizika, himiâ, matematika, Tome 7 (2016) no. 5, pp. 816-834. http://geodesic.mathdoc.fr/item/NANO_2016_7_5_a3/