Effects of screened Coulomb impurities on autoionizing two-electron resonances in spherical quantum dots

In a recent paper [Phys. Rev. B 78, 075316 (2008)], Sajeev and Moiseyev demonstrated that the bound-to-resonant transitions and lifetimes of autoionizing states in spherical quantum dots can be controlled by varying the confinement strength. In the present paper, we report that such control can in some cases be compromised by the presence of Coulomb impurities. It is demonstrated that a screened Coulomb impurity placed in the vicinity of the dot center can lead to bound-to-resonant transitions and to avoided-crossinglike-behavior when the screening of the impurity charge is varied. It is argued that these properties also can have impact on electron transport through quantum dot arrays.

Figure 1

(Color online) Donor impurity $\left(\eta >0\right)$. Upper panels: energy positions of the three lowest states (colored lines) and the position of the $1s$ threshold (solid black line) as the function of the screening strength shown for ${}^{1}S$ (left) and ${}^{1}P$ (right) symmetries. Lower panels: halfwidths of the occurring resonant states. As the position of the second state crosses the threshold, it becomes a bound state and its width vanishes. The values for the range parameter were taken as $\beta =0.21{\left(a_0^{\ast }\right)}^{-2}$ for the ${}^{1}S$ symmetry and $\beta =0.13{\left(a_0^{\ast }\right)}^{-2}$ for the ${}^{1}P$ symmetry. The energies and halfwidths are given both in scaled hartree units (left axis) and meV (right axis) with material parameters of GaAs.

Figure 2

(Color online) Same as in Fig. 1 for an acceptor impurity $\left(\eta <0\right)$. Here, we observe that two states (blue dotted and red solid lines) cross the threshold. However, in the case of ${}^{1}S$ symmetry, the width of the second state (red solid line) is orders of magnitude smaller than the one of the third state and is not shown in the plot since it is not distinguishable from zero on the given scale. The values for the range parameter were taken as $\beta =0.10{\left(a_0^{\ast }\right)}^{-2}$ for the ${}^{1}S$ symmetry and $\beta =0.08{\left(a_0^{\ast }\right)}^{-2}$ for the ${}^{1}P$ symmetry.

Figure 3

(Color online) Left panel: “zoom in” into the plot shown in the upper left panel of Fig. 2. Right panel: energy difference between the two states. The behavior is similar to an avoided crossing. The range parameter of the confinement is $\beta =0.10{\left(a_0^{\ast }\right)}^{-2}$.