Abstract
Understanding how symmetries encode optical polarization information into selection rules in molecules and materials is important for their optoelectronic applications including spectroscopic analysis, display technology, and quantum computation. Here, we extend polarization-dependent selection rules from atoms to solid-state systems with various point groups with the help of the rotational operator for circular polarization and the twofold rotational operator (or reflection operator) for linear polarization. We use these new selection rules to study the optical properties of twisted bilayer graphene quantum dots (TBGQDs), which inherit advantages of graphene quantum dot including its ultrathin thickness, excellent biocompatibility, and shape- and size-tunable optical absorption or emission. We study how the electronic structures and optical properties of TBGQDs rely on size, shape, twist angle, and correlation effects for TBGQDs with 10 different point groups for which we obtain an optical selection rule database. We show how current operator matrix elements identify the generalized polarization-dependent selection rules. Our results show that both the electronic and optical band gaps follow power-law size scalings with a dominant role of the twist angle. We derive an atlas of optical conductivity spectra for both size and twist angle in TBGQDs. As a result of quantum confinement effects, in the atlas a new type of optical conductivity features emerges with multiple discrete absorption frequencies ranging from infrared to ultraviolet energy, allowing for applications in photovoltaic devices and photodetectors. The atlas and size scaling provide a full structure–symmetry-function interrelation and hence offer an excellent basis for the geometrical manipulation of optical properties of TBGQDs as building blocks for novel integrated carbon optoelectronics.
- Received 5 October 2021
- Revised 14 April 2022
- Accepted 3 May 2022
DOI:https://doi.org/10.1103/PhysRevX.12.021055
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
Optical polarization has widespread applications in photodetectors, display technologies, spectroscopic analysis, and telecommunications. Some of these applications require us to understand how symmetries in material structures encode optical polarization into selection rules in molecules and materials. In the past decades, experimental and theoretical investigations have shown that graphene quantum dots are promising for many optical applications. Motivated by recent experimental breakthroughs in twisted bilayer graphene, we develop a theory of the polarization-dependent selection rules and study how the electronic structures and optical properties of twisted bilayer graphene quantum dots (TBGQDs) rely on the material’s size, shape, twist angle, edge structure, and correlation effects.
Using ideas from group theory, we extend polarization-dependent selection rules from atoms to solid-state systems with various symmetries. We construct an optical selection rule database for TBGQDs with ten different types of symmetries. We compile an atlas of both size-dependent and twist-angle-dependent optical spectra of TBGQDs and analyze the power-law scaling of the optical band gap together with selection rules. A new type of optical absorption characteristic emerges with multiple discrete absorption frequencies, ranging from infrared to ultraviolet light, due to quantum confinement effects.
Our findings provide a full structure- and symmetry-function interrelation for geometrical manipulation of TBGQDs in integrated carbon-based optoelectronic devices.
