Symmetry and optical selection rules in graphene quantum dots
| Autor: | E.G. Kavousanaki, Rico Pohle, Keshav M. Dani, Nic Shannon |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Physics
Condensed Matter - Materials Science Condensed matter physics Graphene media_common.quotation_subject Operator (physics) Van Hove singularity Materials Science (cond-mat.mtrl-sci) FOS: Physical sciences 02 engineering and technology 021001 nanoscience & nanotechnology 01 natural sciences Asymmetry Optical conductivity law.invention Zigzag Quantum dot law Quantum mechanics Irreducible representation 0103 physical sciences 010306 general physics 0210 nano-technology media_common |
| Zdroj: | Physical Review B. 97 |
| ISSN: | 2469-9969 2469-9950 |
| Popis: | 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}{($10 \lesssim L \lesssim 50\ \text{nm}$)} 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. 24 pages, 15 figures |
| Databáze: | OpenAIRE |
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