2 research outputs found
Symmetry and optical selection rules in graphene quantum dots
Graphene quantum dots (GQD's) have optical properties which are very
different from those of an extended graphene sheet. In this Article we explore
how the size, shape and edge--structure of a GQD affect its optical
conductivity. Using representation theory, we derive optical selection rules
for regular-shaped dots, starting from the symmetry properties of the current
operator. We find that, where the x- and y-components of the current operator
transform with the same irreducible representation (irrep) of the point group -
for example in triangular or hexagonal GQD's - the optical conductivity is
independent of the polarisation of the light. On the other hand, where these
components transform with different irreps - for example in rectangular GQD's -
the optical conductivity depends on the polarisation of light. We find that
GQD's with non-commuting point-group operations - for example dots of
rectangular shape - can be distinguished from GQD's with commuting point-group
operations - for example dots of triangular or hexagonal shape - by using
polarized light. We carry out explicit calculations of the optical conductivity
of GQD's described by a simple tight--binding model and, for dots of
intermediate size, \textcolor{blue}{()}
find an absorption peak in the low--frequency range of the spectrum which
allows us to distinguish between dots with zigzag and armchair edges. We also
clarify the one-dimensional nature of states at the van Hove singularity in
graphene, providing a possible explanation for very high exciton-binding
energies. Finally we discuss the role of atomic vacancies and shape asymmetry.Comment: 24 pages, 15 figure