[**SYMMETRY CONSTRAINTS AND THE ELECTRONIC STRUCTURES OF A QUANTUM DOT WITH THIRTEEN ELECTRONS**]{}

      G.M. Huang, Y.M. Liu, and C.G. Bao

            The State Key Laboratory of Optoelectronic Materials and Technologies, and

Department of Physics, Zhongshan University,  Guangzhou, 510275, P.R. China

ABSTRACT: The symmetry constraints imposing on the quantum states of a dot with 13 electrons has been investigated. Based on this study, the favorable structures (FSs) of each state has been identified. Numerical calculations have been performed to inspect the role played by the FSs. It was found that, if a first-state has a remarkably competitive FS, this FS would be pursued and the state would be crystal-like and have a specific core-ring structure associated with the FS. The magic numbers are found to be closely related to the FSs.

PACS(numbers): 73.61.-r

1, INTRODUCTION

Modern experimental techniques, e.g., by using electrostatic gates and by etching, allow a certain number of electrons to be confined in semiconductor heterostructures.$^{1-6}$  Such many-electron systems have much in common with atoms, yet they are man-made structures and are usually called ” quantum dot ”.  The number of electrons contained in a dot ranges from a few to a few thousands, they are confined in a domain 