Electronic properties and quasi-zero-energy states of graphene quantum dots

Abstract

In this work, a research has been carried out into 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. 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 toroidal quantum dots (owing to the lack of curvature) the distribution of electron density is similar to 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 graphene quantum dots.

High sensitivity electrochemical DNA sensors for detection of somatic mutations in FFPE samples

“…The Klein resonance is excited by an electric field (for example, the electric field of an electromagnetic pulse). Such areas are called electrostatically-confined graphene p − n (n − p) junctions [19]. The confinement is explained by the occurrence of Klein resonances as a result of Klein oblique tunneling of the massless graphene charge carriers (holes or electrons) through these graphene patches.…”

“…However, the electrical and optical properties of nanostructured graphene-like materials strongly depend on accidental environmental impurities that leads to wide spread of characteristics of the graphene-based devices. Moreover, when scattering and obliquely tunneling through the environmental defects the graphene charge carriers can be confined as Klein resonances [19]. The electrostatical confinement is predicted within the topologically-nontrivial graphene model [20].…”

Application of Quantum Dots in Bio-Sensing, Bio-Imaging, Drug Delivery, Anti-Bacterial Activity, Photo-Thermal, Photo-Dynamic Therapy, and Optoelectronic Devices

“…Firstly, they have remarkable physical characteristics that recognize them from different kinds of QDs; second, they have been effectively used in medical procedures, ultimately, proceeded with use by industry requirements the broad assessment of dangers related with exposure. Electrons are depicted by quantum confinement effects in terms of their energy levels, likely wells, valence band, conduction band, and electron energy band [9]. At the point when the molecule's size is too little to possibly be similar to the frequency of the electron, the quantum confinement effect is noticed.…”

Topologically Tuned Obliquity of Klein-Tunnelling Charged Currents Through Graphene Electrostatically-Confined p - n Junctions

“…In the first case, since the force f ∝ m R has a symmetrical origin it should be linked with a GQD topology. However, the geometrical centrifugal force acting on the GQDs with sphere topology holding a nonzero curvature destroys Bohr-atom-like orbitals formed on resonant trajectories (with an integer number of wave periods on the trajectory) and, oppositely, for the GQDs of toroidal type the interference is possible due to the lack of the geometrical curvature [10]. Besides, for both the whispering-gallery modes and atomic collapse, the wave function of the graphene charge carriers enveloping the geometric obstacle acquires additionally a Berry phase (more precisely, Zak phase).…”