Polarization-dependent selection rules and optical spectrum atlas of twisted bilayer graphene quantum dots

Abstract: Finding out how symmetry encodes optical polarization information into the selection rule in molecules and materials is important for their optoelectronic applications including spectroscopic analysis, display technology and quantum computation. Here, we extend the polarization-dependent selection rules from atoms to solid systems with point group descriptions via rotational operator for circular polarization and $2$-fold rotational operator (or reflection operator) for linear polarization. As a variant of graphene quantum dot (GQD), twisted bilayer graphene quantum dot (TBGQD) certainly inherits GQD's advantages including ultrathin thickness, excellent biocompatibility and shape- and size-tunable optical absorption/emission. We then naturally ask how the electronic structures and optical properties of TBGQDs rely on size, shape, twist angle and correlation effects. We build plentiful types of TBGQDs with $10$ point groups and obtain the optical selection rule database for all types, where the current operator matrix elements identify the generalized polarization-dependent selection rules. Our results show that both of the electronic and optical band gaps follow power-law scalings and the twist angle has the dominant role in modifying the size scaling. We map an atlas of optical conductivity spectra for both size and twist angle in TBGQDs. As a result of quantum confinement effect of finite size, in the atlas a new type of optical conductivity peaks absent in twisted bilayer graphene bulk is predicted theoretically with multiple discrete absorption frequencies from infrared to ultraviolet light, enabling applications on photovoltaic devices and photodetectors. The atlas and size scaling provide a full structure/symmetry-function interrelation and hence offers an excellent geometrical manipulation of optical properties of TBGQD as a building block in integrated carbon optoelectronics.