Resonance states of two-electron quantum dots

Autoionizing resonance states of two-electron quantum dots are studied by using the effective-mass complex-eigenvalue equation approach. It is shown that two-electron quantum dots may have very rich spectra of resonance states. The number of them and their lifetimes depend strongly on the dot size. It is observed that a resonance state may change its character from Feshbach to shape type with the dot size decreasing. Since the resonance states may have very long lifetimes they should not be neglected in the description of transport processes in quantum dots.

Figure 1

Several lowest energy levels of the two-electron QD of radius $15a_0$. (a) Reference 8, (b) this work.

Figure 2

Energies of two-electron bound and resonance states vs dot radius, $R$. (a) and (b) are for $S^e$ and $P^o$ states, respectively. Open circles are used for singlet states and full points for triplet ones. The levels are labeled with the leading electron configurations. The $1s$, $1p$, and $1d$ one-electron levels constitute continua thresholds. The area above the $1s$ level is shadowed to indicate the energy continuum.

Figure 3

Widths of two-electron resonance levels vs the QD radius $R$. The consecutive figures are for the ${}^{1}S^e,{}^{3}S^e,{}^{1}P^o$, and ${}^{3}P^o$ resonances. The labels and open and full symbols are used as in Fig. 2. Diamonds are used for the $1d1f$ states so as to avoid confusion. The resonance width is equal to zero for the critical value of the QD size, proper for a given state. (The curves start at those points.) Vertical bars placed on a given line indicate the QD size values for which the corresponding resonance level crosses the excited one-electron levels (these are consecutively the $1p,1d$, and $2s$ levels) and enters higher continua. Drastic change of the slope of the line associated with such a crossing over the threshold is due to the Feshbach-to-shape change of the resonance character. This does not happen to the $1snl$ states, they omit the Feshbach phase.