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Title: Graphene quantum dots, graphene non-circular n{p{n-junctions: Quasi-relativistic pseudopotential approach
We have constructed a continuous model of graphene quantum dot (GQD) as the hydrodynamic limit of the discrete model of n{p{n graphene junction in the form of a rhombic supercell on the graphene plane. The topological type of the proposed GQD-model corresponds bijectively to the GQD-edge topology and can be similar to a sphere or torus. The Hamiltonian of the discrete model of n{p{n graphene junction is chosen to be the Dirac{Weyl type with one Dirac point and 6 pairs of Weyl nodes{antinodes in the folding-zone approximation. The bending-band structure of the proposed GQD-model is ensured by a GQD pseudopotential barrier, which is given by a set of well pseudopotentials for individual carbon atoms of the GQD. The main speci c feature of the structure of electron levels of both spherical and toroidal GQDs is the self-similar energy bands located subsequently one behind another on the energy scale. The atom-like distribution of the electron density is realized from the geometric viewpoint only for toroidal GQDs due to the absence of the curvature for a torus. Though the quasi-zero-energy band exists for spherical and toroidal GQDs, no electron density is present on this band for toroidal GQDs. This causes the formation of a pseudogap between the hole and electron bands, because of the absence of the electron density at the quantum dot center like the case of an ordinary atom. However, the confinement of the electron density is observed for both spherical and toroidal GQDs.  more » « less
Award ID(s):
1829245
NSF-PAR ID:
10099804
Author(s) / Creator(s):
Date Published:
Journal Name:
NATO science for peace and security series. A, Chemistry and biology
ISSN:
1874-6489
Page Range / eLocation ID:
47-58
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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