We present the derivation and application of an analytical effective potential that is able to describe, in a simple way, the interaction of many electrons confined in low-dimensional structures of realistic size. The effective potential takes into account the contribution of both the electron-electron interaction inside the nanostructure and the quantum confinement by a surrounding material. With this model, we explore the electronic distribution in quantum wells, wires, and dots in the full range from doped to high-doped concentrations. We also use this effective potential to explicitly determine the parameters that trigger the formation of the Wigner molecule in quantum wires. The comparison with experimental data reported in the literature shows the accuracy and reliability of this potential model.

• Received 4 February 2019
• Revised 5 July 2019

DOI:https://doi.org/10.1103/PhysRevB.100.085438