Jahn-Teller distortion of the Wigner molecule in a
three-electron quantum dot and a magnetic field: pair function approach
Manfred Taut
IFW Dresden
|
We considered a two dimensional
three electron quantum dot in a magnetic field in the Wigner limit.
Using a unitary coordinate transformation
of the Hamiltonian (with Coulomb interaction
between the electrons included) into a sum of pair Hamiltonians,
and the Pauli principle for the resulting product of pair functions,
we have shown that the three electrons
in the ground state of the Wigner molecule
form an equilateral triangle (as expected from naive
reasoning) only,
if the state is a quartet ($S=3/2$) and the orbital angular momentum
is a magic quantum number ($|M_L|=3 m \;\; (m=0,1,2,\cdots)$). Otherwise
the triangle is isosceles.
For $|M_L|=3 m+1$ one of the sides is
longer and for $|M_L|=3 m-1$