Abstract
In this paper, research has been carried out on the electronic properties of nanostructured graphene. We focus our attention on trapped states of the proposed systems such as spherical and toroidal graphene quantum dots (GQDs). Using a continuum model, by solving the Dirac-Weyl equation, and applying periodic boundary conditions of two types, i.e., either with zigzag edges only or with both armchair and zigzag edges, we obtain analytical results for energy levels yielding self-similar energy bands located subsequently one after another on the energy scale. Only for the toroidal quantum dot (owing to the lack of curvature) the distribution of electron density is like Bohr atomic orbitals. However, although the quasi-zero-energy band exists for both spherical and toroidal quantum dots, no electron density is present on this band for the toroidal quantum dot. 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 in the case of an ordinary atom. Conversely, the confinement of the charge-carrier density is observed for both geometries of GQDs.
Highlights
Nanodimensional monolayer graphene patches are promising as a basis for the development of quantum devices
The dependence is similar to local density of states (LDOS) for a tight-binding Hamiltonian of graphene charge carriers moving in a potential of the Thomas–Fermi atom model [5]
For the toroidal graphene quantum dot, the chargecarrier density is absent on the quasi-zero-energy band due to a destructive interference of the states
Summary
Nanodimensional monolayer graphene patches are promising as a basis for the development of quantum devices. The dependence is similar to local density of states (LDOS) for a tight-binding Hamiltonian of graphene charge carriers moving in a potential of the Thomas–Fermi atom model [5] According to this estimate, the quantum dot is an artificial atom with a huge number of electrons, as the effective electric charge of Coulomb potential or the Coulomb coupling β = (Z/ G)αc/vF , which confines charge carriers in the tip-induced junction, takes on values typical for a supercritical regime of ultra-heavy atoms. Assuming that the effects of Klein tunneling will always distort the electrostatic confinement of massless charge carriers, the variety of solutions to the problem of pseudo-Dirac fermions in electrostatically confined graphene p-n(n-p) junctions can be narrowed down to the subvariety of levels localized near the Fermi level (quasi-zero-energy levels or whispering gallery modes). We discover two topologically different scenarios of the confinement in a quantum dot
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
