Scrambling and gate-induced fluctuations in realistic quantum dots

We evaluate the magnitude of two important mesoscopic effects using a realistic model of typical quantum dots. “Scrambling” and “gate effect” are defined as the change in the single-particle spectrum due to added electrons or gate-induced shape deformation, respectively. These two effects are investigated systematically in both the self-consistent Kohn-Sham (KS) theory and a Fermi liquidlike Strutinsky approach. We find that the genuine scrambling effect is small because the potential here is smooth. In the KS theory, a key point is the implicit inclusion of residual interactions in the spectrum; these dominate and make scrambling appear larger. Finally, the gate effect is comparable in the two cases and, while small, is able to cause gate-induced spin transitions.

Figure 1

(Color online) Illustration of scrambling and gate effects in Coulomb blockade conductance fluctuations.

Figure 2

(Color online) Upper panel, schematic of the shape of the top confining gate used in this study. Negative voltages are imposed on the shaded region, depleting the electrons underneath so that the motion of electrons is confined to a small region. To obtain enough statistics, 24 different irregular confining shapes are generated by taking different values of $X_1$, $X_2$, $Y_1$, and $Y_2$. Lower panel, the nearest neighbor spacing distribution of the single-particle levels calculated in the Thomas–Fermi effective potential (histogram) compared to the Wigner surmise distribution (line).

Figure 3

(Color online) Scrambling magnitude as a function of $\delta N$ (upper) and gate fluctuation as a function of $\delta N^{*}$ (lower) from the TF (filled) or KS (empty) single particle spectra with $z_d=15\mathrm{nm}$ (circles) or 50 nm (triangles). Inset, the result of a universal random matrix model.