Group Theoretical Analysis of Symmetry Breaking in Two-Dimensional Quantum Dots

Abstract

We present a group theoretical study of the symmetry- broken unrestricted Hartree-Fock orbitals and electron densities in the case of a two-dimensional N-electron single quantum dot (with and without an external magnetic field). The breaking of rotational symmetry results in canonical orbitals that (1) are associated with the eigenvectors of a Huckel hamiltonian having sites at the positions determined by the equilibrium molecular configuration of the classical Ν'- electron problem, and (2) transform according to the irreducible representations of the point group specified by the discrete symmetries of this classical molecular configuration. Through restoration of the total-spin and rotational symmetries via projection techniques, we show that the pointgroup discrete symmetry of the unrestricted Hartree-Fock wave function underlies the appearance of magic angular momenta (familiar from exact-diagonalization studies) in the excitation spectra of the quantum dot.

Keywords: 73, 73.21-b, 73.21.La