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arXiv · 0710.4325

Three-electron anisotropic quantum dots in variable magnetic fields: exact results for excitation spectra, spin structures, and entanglement

Yuesong Li·Constantine Yannouleas·Uzi Landman
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Abstract

Exact-diagonalization calculations for N=3 electrons in anisotropic quantum dots, covering a broad range of confinement anisotropies and strength of inter-electron repulsion, are presented for zero and low magnetic fields. The excitation spectra are analyzed as a function of the strength of the magnetic field and for increasing quantum-dot anisotropy. Analysis of the intrinsic structure of the many-body wave functions through spin-resolved two-point correlations reveals that the electrons tend to localize forming Wigner molecules. For certain ranges of dot parameters (mainly at strong anisotropy), the Wigner molecules acquire a linear geometry, and the associated wave functions with a spin projection S_z=1/2 are similar to the representative class of strongly entangled states referred to as W-states. For other ranges of parameters (mainly at intermediate anisotropy), the Wigner molecules exhibit a more complex structure consisting of two mirror isosceles triangles. This latter structure can be viewed as an embryonic unit of a zig-zag Wigner crystal in quantum wires. The degree of entanglement in three-electron quantum dots can be quantified through the use of the von Neumann entropy.

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Yuesong Li, Constantine Yannouleas, Uzi Landman. 2007-10-23. Three-electron anisotropic quantum dots in variable magnetic fields: exact results for excitation spectra, spin structures, and entanglement. https://doi.org/10.1103/physrevb.76.245310

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