In this paper, we perform a systematic study on the electronic, magnetic, and transport properties of the hexagonal graphene quantum dots (GQDs) with armchair edges in the presence of a charged impurity using two different configurations: (1) a central Coulomb potential and (2) a positively charged carbon vacancy. The tight-binding and the half-filled extended Hubbard models are numerically solved and compared with each other in order to reveal the effect of electron interactions and system sizes. Numerical results point out that off-site Coulomb repulsion leads to an increase in the critical coupling constant to β c = 0.6 for a central Coulomb potential. This critical value of β is found to be independent of the GQD size, reflecting its universality even in the presence of electron-electron interactions. In addition, a sudden downshift in the transmission peaks shows a clear signature of the transition from subcritical β < β c to the supercritical β > β c regime. On the other hand, for a positively charged vacancy, collapse of the lowest bound state occurs at β c = 0.7 for the interacting case. Interestingly, the local magnetic moment, induced by a bare carbon vacancy, is totally quenched when the vacancy is subcritically charged, whereas the valley splittings in electron and hole channels continue to exist in both regimes.
Reciprocal space mapping (RSM) has been widely utilized to find out the microstructure and deviations from ideal crystal structures, present in materials ranging from polycrystalline to single-crystalline [1]. RSM can deliver further structural information as compared to conventional methods such as rocking curve (RC) scan due to its two-dimensional (2D) characteristics [2]. This particularly provides a significant advantage when applied to epitaxial thin films having large lattice mismatches. Nondestructive measurement of the threading-dislocation (TD) densities, for instance, relies on prediction of individual parameters, such as domain tilt and twist, of a mosaic layer structure [3]. In addition to the large lattice mismatch, some epitaxial heterostructures have also the low-symmetry surface characteristics. CdTe/(2 1 1)B GaAs is obviously one of the outstanding examples of these types of structures. Structural analysis of the high-index oriented zinc-blende epitaxial layers when combined with the large lattice mismatch becomes much more challenging. Furthermore, the surface normal of epilayer lattice tilts approximately 3° with respect to that of substrate [4]. Each one of these factors make the structure being examined extremely difficult to analyze, especially with the traditional x-ray diffraction (XRD) methods. As a result, a limited number of studies so far have been dedicated to understanding the structural properties of this heterostructure [5][6][7][8]. The common point of all these studies is that they were carried out in real space. However, one advantageous option can be mapping in reciprocal space to characterize such heterostructures. At present, the technique has been separately applied to the high-index orientation [9] or to the large lattice mismatched heterostructures [10].In this letter, the RSM technique is effectively employed to study the lattice tilting, the lattice mismatches, the shear strain produced by the low-symmetry surface and the screw dislocation density of CdTe epilayer grown on (2 1 1) oriented GaAs substrate.
Experimental procedure
Molecular beam epitaxy (MBE) growth of CdTeThe growth details were similar to those described elsewhere [11,12]. Briefly, CdTe epilayer was grown by molecular beam epitaxy (MBE) system operated in a class 1000 cleanroom environment on a 3-inch epi-ready, semi-insulating (2 1 1)B GaAs wafer after thermal stripping of the oxide layer. Initially, a nucleation layer also
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