Comparison of methods for computing the exchange energy in laterally coupled quantum dots

Abstract

We calculate the exchange energy in two dimensional laterally coupled quantum dots using Heitler-London, Hund-Mullikan and variational methods. We assess the quality of these approximations in zero and finite magnetic fields comparing against numerically exact results. We find that surprisingly, the Hund-Mullikan method does not offer any significant improvement over the much simpler Heitler-London method, whether at large or small interdot distances. Contrary to that, our variational ansatz proves substantially better. In a single dot at finite magnetic field, all approximate methods fail. This reflects the qualitative change of the single electron ground state from non-degenerate (harmonic oscillator) to highly degenerate (Landau level). However, we find that the magnetically induced failure does not occur in the most important, double-dot, regime.

Main results of my Bachelor's work. June 2009, Bratislava. 6 pages, 7 figures

References in corpus (4)

• Spin properties of single electron states in coupled quantum dots
• Theory of anisotropic exchange in laterally coupled quantum dots
• Failure of standard approximations of the exchange coupling in nanostructures
• Spin-orbit coupling and anisotropic exchange in two-electron double quantum dots