1. (a) Bravais lattice of graphene whose the lattice constant is 2.46Å46˚46Å, (b) inplane σ, which are consisting of the sp 2 hybridization, and out of plane π bonds in graphene, and (c) 3D dispersion relation of graphene shows the valance and conduction bands. Here, the inequivalent K and K' points is also shown (Source: (Yazdi et al. (2016)).

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... two atoms leads to the formation of the valance (π) and conduction (π * ) bands. In the tight binding (TB) approximation, dispersion relation of graphene shows that the valance and conduction bands touch each 1 other at six points in the Brillouin zone, which indicates that graphene is a zero-band-gap semiconductor ( Neto et al. (2009)), see Fig. 1.1(a)-(c). Graphene, as a two-dimensional (2D) allotrope of carbon, is of significant interest starting from its first experimental isolation ( Novoselov et al. (2004)), since a novel sp 2 -hybridized carbon network has significant physical properties ( Neto et al. (2009)) as compared to other carbon ...

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... this thesis, in the presence of experimentally relevant charged impurities, we will study the electronic magnetic, and transport properties of the hexagonal GQDs with armchair edges and the triangular GQDs with zigzag edges, which are illustrated in Fig. 1.2(a) and Fig. 1.2(b), respectively. In our numerical calculations, we obtained these GQDs by cutting from an infinite monolayer ...

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... this thesis, in the presence of experimentally relevant charged impurities, we will study the electronic magnetic, and transport properties of the hexagonal GQDs with armchair edges and the triangular GQDs with zigzag edges, which are illustrated in Fig. 1.2(a) and Fig. 1.2(b), respectively. In our numerical calculations, we obtained these GQDs by cutting from an infinite monolayer ...

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... regularization results in a larger critical threshold of Z c ∼ 172 above which the wave function becomes a narrow resonance with a finite lifetime in compliance with Fano s formalism. The behaviour of atomic collapse states as a function of nuclear charge Z for the real atoms is shown in Fig.1.4 (Reinhardt and Greiner (1977)). ...

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... n and m are integer numbers, and the vector b goes from the A (red) sublattice to the B (blue) sublattice in the unit cell, as shown in Fig. 2.1. In this thesis, we model the non-interacting fermions with the help of TB approach, whereas we will use the mean field Hubbard model to describe the π z dynamics of the interacting fermions. The latter will be introduced in the next section. As for the lattice, two dimensional honeycomb lattice can be constructed via these primitive ...

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... <n iσ >'s are calculated by summing up all states lying below Fermi level. Here, the total spin of the system is given by S = i < s z i > (Yazyev (2010)). Starting from Eq. 2.37, the staggered magnetization as an order parameter of the antiferromagnetism is numerically calculated from ...

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... Fig. 1(c)] that the lowest bound state enters the supercritical regime at β c = 0.5, which is the same as of bulk graphene. In compliance with our non-interacting fermion results, the critical wave functions of the circular GQDs merge into negative energies at the value of β c = 0.5 within the effective mass approximation with an infinite mass ...

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... magnitude in electron and hole channels within the TB method, see the vertical arrows in Fig. 4.1(b). At the FL, we have a pronounced vacancy peak due to intervalley scattering caused by a bare carbon vacancy. This vacancy state splits into up and down vacancy states with equal spin probability and the occupation of <n ↓ > = 1 and <n ↑ > = 0 as shown in Fig. 4.1(c) when the electron-electron interactions are turned on within the MFH ...