Artificial quantum-dot Helium molecules: Electronic spectra, spin structures, and Heisenberg clusters

Details Artificial quantum-dot Helium molecules: Electronic spectra, spin structures, and Heisenberg clusters Artificial quantum-dot Helium molecules: Electronic spectra, spin structures, and Heisenberg clusters

2009-07-09

arxiv.org/abs/0907.1571v1

Phys. Rev. B 80, 045326 (2009)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

REVTEX 4. 18 pages with 10 figures. Accepted for publication in Physical Review B. This paper incorporates material from arXiv

Scientific paper

10.1103/PhysRevB.80.045326

Energy spectra and spin configurations of a system of N=4 electrons in lateral double quantum dots (quantum dot Helium molecules) are investigated using exact diagonalization (EXD), as a function of interdot separation, applied magnetic field (B), and strength of interelectron repulsion. As a function of the magnetic field, the energy spectra exhibit a low-energy band consisting of a group of six states, with the number six being a consequence of the conservation of the total spin and the ensuing spin degeneracies for four electrons. The energies of the six states appear to cross at a single value of the magnetic field, and with increasing Coulomb repulsion they tend to become degenerate, with a well defined energy gap separating them from the higher-in-energy excited states. The appearance of the low-energy band is a consequence of the formation of a Wigner supermolecule, with the four electrons (two in each dot) being localized at the vertices of a rectangle. Using spin-resolved pair-correlation distributions, a method for mapping the complicated EXD many-body wave functions onto simpler spin functions associated with a system of four localized spins is introduced. Detailed interpretation of the EXD spin functions and EXD spectra associated with the low-energy band via a 4-site Heisenberg cluster (with B-dependent exchange integrals) is demonstrated. Aspects of spin entanglement, referring to the well known N-qubit Dicke states, are also discussed.

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