Model for a biexciton in a lateral quantum dot based on exact solutions for the Hookean H₂ molecule. I. Theoretical aspects

Abstract

ABSTRACT:We present here a model for the non-Born-Oppenheimer description of the biexcitonic complex X 2 (eehh) trapped in laterally-coupled quantum dot system. We define a zeroth-order Hamiltonian which allows us, under certain conditions on the masses and coupling constants, to decouple the problem. We show that the zeroth-order wavefunctions and energies can be described using the exact solutions for the Hookean model for the H 2 molecule [Ludeña et al., J Chem Phys 2005, 123, 024102]. We also apply this Hookean model to the description of the excitonic complexes X + 2 (ehh), X − (eeh), and to the single exciton X(eh) and analyze the dependence of the total non-Born-Oppenheimer zeroth-order energies, and binding energies for these sytems with the mass ratio σ . The general features of the results obtained using this Hookean model agree quite well with those of more elaborate calculations.