Shape, Size - Related Quantum Structure Of Graphene Quantum Dots

Novoselov successfully manufactured the one-atom-thick two-dimensional honeycomb lattice of carbon atoms by the mechanical stripping method in 2004,which shows extraordinary properties in optics, electricity, mechanics and thermal physics. However, owing to the lack of a bandgap, its electronic and opto-electronic applications have been limited to some extent. Recent advances in material process technology have enabled the preparation of graphene quantum dots(GQDs) when the size of graphene gets less than 10 nm. There have been tremendous advances in theoretical investigations into electronic structure of GQDs with kinds of shapes(such as circular, hexagonal, triangular and so on) under different boundary condition(zigzag, armchair, infinite-mass) utilizing the tight-binding model or continuum approach respectively. As a quasi-zero-dimensional nanostructure material, it will generate a series of novel physical properties because the effect of different sizes,shapes and boundary conditions of GQDs, especially, it will have great potentials in light emitting, which have attracted much attention.In this article, we mainly do the corresponding research which is represented as follows:First, we describe the electronic structure of circular GQDs by the tight-binding model, and the Dirac equation of electron motion can be built. We get the numerical solution by the Finite Difference Method(FDM) on armchair and zigzag graphene quantum disk, which is the electron energy state of armchair and zigzag graphene quantum disk, respectively. Besides, we also get the analytic solution of Dirac equation by infinite-mass boundary condition(IMBC), which can obtain the electron energy state in this approximate boundary condition as well.Second, for triangular GQDs, we make the description of electronic structure by using The generalized gradient approximation method based on density functional theory. We do the geometry optimization on zigzag triangular GQDs by PW91, anddo the optimization on spin multiplicities using spin-unrestricted method. The state of charge occupancy and spin in orbital can be obtained by Mulliken. The different electronic states of orbital 2s and 2p can be depicted by the double-number polarization vector, and the polarization of orbital can be analyzed by wavefunction of orbital 3d. Besides, Z10-GNGs can be used to analyze the total electronic density and separate electronic density.The result show that there exists separate energy levels in GQDs. With the radius of disks larger, with lower energy of these two kinds quantum disks, with narrower the bandgap, with larger the intensity of energy states, when the magnetic field is absent. The symmetry of zigzag quantum disk will be broken after adding an orthogonal magnetic field. The electronic state density is size-dependent in triangular zigzag GQDs. Our results will provide theoretical guidance for experimental design of GQDs, and the application of GQDs in the optoelectronics research field.