3 research outputs found
Edge-dependent selection rules in magic triangular graphene flakes
The electronic shell and supershell structure of triangular graphene quantum
dots has been studied using density functional and tight-binding methods. The
density functional calculations demonstrate that the electronic structure close
to the Fermi energy is correctly described with a simple tight-binding model
where only the p_z orbitals perpendicular to the graphene layer are included.
The results show that (i) both at the bottom and at the top of the p_z band a
supershell structure similar to that of free electrons confined in a triangular
cavity is seen, (ii) close to the Fermi level the shell structure is that of
free massless particles, (iii) triangles with armchair edges show an additional
sequence of levels ('ghost states') absent for triangles with zigzag edges
while the latter exhibit edge states, and (iv) the observed shell structure is
rather insensitive to the edge roughness
Electronic structure of triangular, hexagonal and round graphene flakes near the Fermi level
The electronic shell structure of triangular, hexagonal and round graphene
quantum dots (flakes) near the Fermi level has been studied using a
tight-binding method. The results show that close to the Fermi level the shell
structure of a triangular flake is that of free massless particles, and that
triangles with an armchair edge show an additional sequence of levels ("ghost
states"). These levels result from the graphene band structure and the plane
wave solution of the wave equation, and they are absent for triangles with an
zigzag edge. All zigzag triangles exhibit a prominent edge state at the Fermi
level, and few low-energy conduction electron states occur both in triangular
and hexagonal flakes due to symmetry reasons. Armchair triangles can be used as
building blocks for other types of flakes that support the ghost states. Edge
roughness has only a small effect on the level structure of the triangular
flakes, but the effect is considerably enhanced in the other types of flakes.
In round flakes, the states near the Fermi level depend strongly on the flake
radius, and they are always localized on the zigzag parts of the edge