Dimensionality effect on two-electron energy spectrum: A fractional-dimension-based formulation

• We report the two-electron eigenenergies in a quantum dot with anisotropic parabolic confinement.
• Our model is versatile enough to consider changes in the dimension space from 3 to 2 and 2 to 1.
• The two-electron structure is calculated in integer and fractional dimensional spaces.
• The two-electron energy structure is sensitive to the quantum dot size and morphology changes.
• The electron–electron Coulomb interaction is strongly dependent on the space dimensionality.

We analyze the spectrum of two-electron quantum dot with anisotropic parabolic confinement by using the fractional-dimension formulation which allows us to reduce the two-particle problem to two equations for independent particles in an effective space with variable dimension, ranging between two and three for ellipsoidal-shaped quantum dots and between one and two for elliptical-shaped quantum disks. The dependencies of energy levels on the heterostructure sizes for quantum dots, disks and wires are presented.