Near-threshold properties of the electronic density of layered quantum dots

We present a way to manipulate an electron trapped in a layered quantum dot based on near-threshold properties of one-body potentials. First, we show that potentials with a simple global parameter allow the manipulation of the wave function, changing its spatial localization. This phenomenon seems to be fairly general and could be implemented using current quantum-dot quantum-well technologies and materials if a proper layered quantum dot is designed. So, we propose a model layered quantum dot that consists of a spherical core surrounded by successive layers of different materials. The number of layers and the constituent materials are chosen to highlight the near-threshold properties. The manipulation of the spatial localization of the electron in a layered quantum dot yields results consistent with actual experimental parameters.

Figure 1

Electronic density as a function of $r$ for the ground-state Hamiltonian [Eq. (1)]. The dark green vertical dash-dotted lines show the zeros of the potential defined in Eq. (2). The black continuous line shows the electronic density for $W_0=0.3$ a.u., the black dashed line shows the electronic density for $W_0=0.2$ a.u., red dash-dotted line shows the calculation for $W_0=0.16$ a.u., and the blue dotted line shows the electronic density for $W_0=0.14$ a.u. The inset shows the same electronic densities and the potential at a different scale. The dark green dash-dotted curve corresponds to the potential, which is plotted in $W_0$ units.

Figure 2

(a) Position where the electronic density achieves its maximum value ($r_{\max }$) as a function of $W_0$. The vertical dashed line shows the critical ionization value $W_0^{\left(c\right)}$. (b) The well occupation probability $I_n$ as a function of $W_0$. For large values of $W_0$ the ground state wave function is localized around the origin, so only $I_1$ is appreciable. For smaller values of $W_0$, $I_1$ drops to zero and the successive wells became occupied. Near the threshold many wells are occupied but $I_n\to 0,\forall n$.

Figure 3

The upper panel shows the contour map of the electronic density as a function of the coordinate $r$ and the strength potential $W_0$ for the potential defined in Eq. (2). A zoom of this figure is shown in the lower panel. The figures show how the electronic density's higher peak moves as $W_0$ decreases. Note that for certain values of $W_0$ the electronic density has one, two, or three peaks.

Figure 4

The electronic density for two different layered quantum dots. The electronic density in panel (a) corresponds to a CdS/HgS/CdS/HgS/CdS structure ($r_c=2$ nm), while panel (b) corresponds to a HgS/CdS/HgS/CdS one ($r_c=0$ nm). The structures are shown as ring patterns (after the last HgS layer we consider that we have a very long CdS barrier). Panel (c) shows the behavior of the position where the electronic density achieves its maximum value ($\Delta r=r_{\max }-r_c$), measured with respect to the inner radius of the first potential well as a function of the core width $r_c$. For large enough values of the CdS core the electronic density maximum lies in the first potential well, as shown in panel (a). When the radius of the CdS core approaches 0.5 nm the maximum of the electronic density jumps to the second potential well, as shown by the abrupt change in $\Delta r$ in panel (c). The green dashed line in (a) and (b) shows the steplike potential.

Figure 5

The electronic density for three different CdS/HgS/CdS/HgS/CdS layered quantum dots. The electronic density in panel (a) corresponds to $r_c=5$ nm, while for panel (b) $r_c=1$ nm and panel (c) $r_c=0.1$ nm. The dark green dashed line in (a), (b), and (c) shows the steplike potential.

Figure 6

Panel (a) shows the oscillator strength as a function of the core width $r_c$ calculated using Eq. (6) for the ground and lower excited states with $l=1$. Panel (b) shows the behavior of the position where the electronic densities achieves their maximum values ($\Delta r=r_{\max }-r_c$), measured with respect to the inner radius of the first potential well as a function of the core width $r_c$. For large enough values of the CdS core the electronic density maxima lie in the first potential well. When the radius of the CdS core approaches $1.8$ nm ($0.23$ nm) the maximum of the excited sate (ground state) electronic density jumps to the second potential well, as shown by the abrupt change in $\Delta r$.