Polarization-Dependent Selection Rules and Optical Spectrum Atlas of Twisted Bilayer Graphene Quantum Dots

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.