Distortion of Wigner molecules: a pair function approach

Abstract

We considered a two-dimensional three-electron quantum dot in a magnetic field in theWigner limit. A unitary coordinate transformation decouples the Hamiltonian(with Coulomb interaction between the electrons included) into a sum of threeindependent pair Hamiltonians. The eigensolutions of the pair Hamiltonian provide aspectrum of pair states. Each pair state defines the distance of the two electronsinvolved in this state. In the ground state for given pair angular momentumm, this distance increaseswith increasing |m|. The pair states have to be occupied under consideration of the Pauli exclusion principle,which differs from that for one-electron states and depends on the total spinS and the total orbital angular momentum (the sum over all pair angular momenta). We have shown that thethree electrons in the ground state of the Wigner molecule form anequilateral triangle (as might be expected) only if the state is a quartet(S = 3/2) and the orbital angular momentum is a magic quantum number(ML = 3m;m = integer). Otherwise the triangle in the ground state is isosceles. ForML = 3m+1 one of the sidesis longer and for ML = 3m−1 one of the sides is shorter than the other two.