Symmetric Eigen-Wavefunctions of Quantum Dot Bound States Resulting from Geometric Confinement

Self-assembled semiconductor quantum dots possess an intrinsic geometric symmetry due to the crystal periodic structure. In order to systematically analyze the symmetric properties of quantum dots' bound states resulting only from geometric confinement, we apply group representation theory. We label each bound state for two kinds of popular quantum dot shapes: pyramid and half ellipsoid with the irreducible representation of the corresponding symmetric groups, i.e., C_4v and C_2v, respectively. Our study completes all the possible irreducible representation cases of groups C_4v and C_2v. Using the character theory of point groups, we predict the selection rule for electric dipole induced transitions. We also investigate the impact of quantum dot aspect ratio on the symmetric properties of the state wavefunction. This research provides a solid foundation to continue exploring quantum dot symmetry reduction or broken phenomena because of strain, band-mixing and shape irregularity. The results will benefit the researchers who are interested in quantum dot symmetry related effects such as absorption or emission spectra, or those who are studying quantum dots using analytical or numerical simulation approaches.