Two-dimensional C/BN core/shell structures

Single-layer core-shell structures consisting of graphene as the core and hexagonal boron nitride as the shell are studied using the first-principles plane-wave method within density functional theory. Electronic energy level structure is analyzed as a function of the size of both core and shell. It is found that the confinement of electrons in a two-dimensional graphene quantum dot is reduced by the presence of a boron nitride shell. The energy gap is determined by the graphene states. Comparison of round, hexagonal, rectangular, and triangular core-shell structures reveals that their electronic and magnetic states are strongly affected by their geometrical shapes. The energy level structure, energy gap, and magnetic states can be modified by external charging. The core part acts as a two-dimensional quantum dot for both electrons and holes. The of extra electron intake capacity of these quantum dots is shown to be limited by the Coulomb blockade in two dimensions.

Figure 1

(a) Ball-and-stick representation of single-layer C/BN CS structure. The presented structure is denoted as CS($r_1=3$, $r_2=5$). Here radii $r_1$ and $r_2$ are defined as the number of hexagonal atomic rings formed by C atoms and total number of hexagonal rings, respectively. Note that for $r_2⩽5$ the atoms enclosed by a circle of this radius make a hexagonal structure. (b) The energy gap between the HOMO and LUMO levels for hexagonal structures having various $r_1$ and $r_2$ values. (c) Energy gap trends for round graphene patches with various radii and edge patterns calculated from first principles and using the nearest-neighbor tight-binding approximation. A ball-and-stick representation of these round structures is presented in the inset.

Figure 2

Energy level diagram for the fully relaxed hexagonal structure of C atoms, the hexagonal shell structure of BN, and the CS structure, which is formed by the combination of the first two structures. Isosurface charge densities are projected on specific states of CS(2,4) structure. Single arrows correspond to the nondegenerate states. Charge densities of the doubly degenerate band-edge states are shown by two arrows. The $+$ sign between these two arrows denotes that the plotted charge density profile is the average value of two degenerate states. All plots have the same isosurface values. The zero of energy is set to the middle of the gap between the HOMO and the LUMO. The energy gap region is shaded.

Figure 3

(a) Comparison of hexagonal (C${}_{54}$B${}_{48}$N${}_{48}$H${}_{30}$) and rectangular (C${}_{54}$B${}_{46}$N${}_{46}$H${}_{32}$) CS structures. C and BN regions are delineated on the isosurface charge density plots. Band-edge states of hexagonal structure are doubly degenerate, while in the rectangular structure this degeneracy is lifted. (b) Comparison of hexagonal (C${}_{24}$B${}_{36}$N${}_{36}$H${}_{24}$) and triangular (C${}_{22}$B${}_{36}$N${}_{36}$H${}_{24}$) CS structures. Split majority and minority spin states of the triangular structure are shown side by side. Band-edge states of both hexagonal and triangular structures are doubly degenerate. The zero of energy is set at the middle of the energy gap between the HOMO and the LUMO and is shown by dash-dotted lines. The energy gap region is shaded.

Figure 4

(a) Energy level diagram for pristine and charged CS(2,4) structures. The minority and majority spin levels are shown at the left- and right-hand sides of the same plot, respectively. The filled states are shown by dark (red) lines and the empty states are shown by light (green) lines. The energy level of the edge and vacuum states mentioned in the text are shown by dash-dotted (blue) and dashed (black) lines, respectively. In all plots except the case of two electrons injected, the zero of energy is set to the local potential value at the place farthest from the surface. The reason for this exception and the definition of zero energy for this plot is explained in the text. (b) Top: planar-averaged local potential difference between charged and pristine structures, plotted along the axis perpendicular to the surface. Bottom: planar-averaged linear charge density for specific states, plotted along the axis perpendicular to the structures. Contour plots of specific states averaged along this axis are shown on the honeycomb structure.