Wigner molecules in polygonal quantum dots: A density functional study

TL;DR

This study uses density functional theory to explore electron arrangements in polygonal quantum dots, revealing how electron localization and spin symmetry breaking depend on dot size and shape, with implications for understanding Wigner molecule formation.

Contribution

It provides a detailed analysis of Wigner molecule formation and spin symmetry breaking in polygonal quantum dots using density functional theory, extending previous exact studies.

Findings

Wigner molecules form in two-electron systems consistent with exact results.

Spin symmetry breaking occurs in polygonal geometries during DFT calculations.

Transition to crystallized states aligns with electron number and is shape-insensitive.

Abstract

We investigate the properties of many-electron systems in two-dimensional polygonal (triangle, square, pentagon, hexagon) potential wells by using the density functional theory. The development of the ground state electronic structure as a function of the dot size is of particular interest. First we show that in the case of two electrons, the Wigner molecule formation agrees with the previous exact diagonalization studies. Then we present in detail how the spin symmetry breaks in polygonal geometries as the spin density functional theory is applied. In several cases with more than two electrons, we find a transition to the crystallized state, yielding coincidence with the number of density maxima and the electron number. We show that this transition density, which agrees reasonably well with previous estimations, is rather insensitive to both the shape of the dot and the electron number.