Logarithmically perturbed two dimensional oscillator model of a quantum-dot nanostructure

Abstract

We present a logarithmically perturbed two-dimensional isotropic oscillator model of a quantum-dot nanostructure. The logarithmic potential has an ionic line charge physical origin. We estimate the magnitude of this line charge and we obtain the matrix elements required by perturbation theory. The measured ground-state energy depression for a GaAs/AlGaAs/InGaAs heterostructure can be quantitatively accounted for by the model (although not uniquely). We include the effects of nonzero angular momentum states, which play a significant role in determining the dot current–voltage curves. We mention the immediate selection rule imposed by a perturbing potential of rotational symmetry, together with further analytic results.