Electrons confined in quantum dots can form Island-like space structures called Wigner molecules. We discuss the ground-state properties of two-dimensional Wigner molecules. In particular, we consider the formation of different phases (isomers) of the Wigner molecules at high magnetic fields. The JV-electron system, confined in the quantum dot and subject to a sufficiently strong magnetic field, forms a fully spin-polarized maximum density droplet (MDD). At high enough magnetic field the MDD decays and the Wigner molecule is formed with an island-like electron distribution. For JV > 6 several different phases of the JV-electron Wigner molecule have been predicted. At extremely high magnetic fields, the spatial distribution of the electrons is the same as that in a classical system of equal point charges. Possible mechanisms of MDD breakdown, i.e. hole formation in the occupation number distribution and an edge reconstruction, are addressed. We also consider the creation of Wigner molecules without applying an external magnetic field in an electron system confined within a single quantum dot of large enough size and compare these Wigner molecules with artificial molecules formed in coupled quantum dots. Possible experimental evidence is examined for the formation of different phases of Wigner molecules.
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