Spin and Conductance-Peak-Spacing Distributions in Large Quantum Dots: A Density-Functional Theory Study

We use spin-density-functional theory to study the spacing between conductance peaks and the ground-state spin of 2D model quantum dots with up to 200 electrons. Distributions for different ranges of electron number are obtained in both symmetric and asymmetric potentials. The even/odd effect is pronounced for small symmetric dots but vanishes for large asymmetric ones, suggesting substantially stronger interaction effects than expected. The fraction of high-spin ground states is remarkably large.

Figure 1

Addition energy as a function of electron number. (a) Raw addition energy data (solid) and its polynomial fit (dashed) to remove the change in classical charging energy. (b) Addition energies scaled by the mean level spacing after removing smooth part ($\lambda =0.6$ and $\gamma =0$).

Figure 2

Distributions of peak spacing, $s$, for even (solid) and odd (dashed) $N$. The columns correspond to the different ranges of electron number indicated, while the first row [(a)–(c)] is for a symmetric external potential and the second for asymmetric [(d)–(f)]. The inset of each figure shows the corresponding spin distribution for $N$ even (solid) and odd (shaded). Both the lack of even/odd effect and the large spin in panel (f) is striking and indicates an unexpectedly large effective electron-electron interaction. (A sliding window is used in estimating the probability density, yielding a smooth curve rather than a histogram; each curve is made from 150 data points using a Gaussian window of width 0.3.)

Figure 3

Distributions of the single-particle level spacing (scaled by the mean) and the IPR from Kohn-Sham calculations and from random matrix theory. (a) The distribution of SPLS calculated from top KS orbital energies for symmetric (solid) and asymmetric (dashed) case, respectively. (b) The distribution of IPR calculated from top-level KS orbital wave functions for symmetric (solid) and asymmetric (dashed) case, respectively. (c) The distributions of SPLS for a single GOE (dashed) and the superposition of four GOE (solid) according to RMT. (d) The distributions of IPR calculated from the eigenvectors of real symmetric random matrix with dimension $M=20$ (solid) and $M=80$ (dashed).