Correlation energy of anisotropic quantum dots

Abstract

We study the $D$-dimensional high-density correlation energy $\Ec$ of the singlet ground state of two electrons confined by a harmonic potential with Coulombic repulsion. We allow the harmonic potential to be anisotropic, and examine the behavior of $\Ec$ as a function of the anisotropy ${\alpha }^{-1}$. In particular, we are interested in the limit where the anisotropy goes to infinity ($\alpha \to 0$) and the electrons are restricted to a lower-dimensional space. We show that tuning the value of $\alpha$ from 0 to 1 allows a smooth dimensional interpolation and we demonstrate that the usual model, in which a quantum dot is treated as a two-dimensional system, is inappropriate. Finally, we provide a simple function which reproduces the behavior of $\Ec$ over the entire range of $\alpha$.

5 pages, 2 figures, 1 table, submitted to Phys. Rev. A

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