Signatures of lateral coupling of double quantum dots in the exciton photoluminescence spectrum

We study an electron-hole pair in laterally coupled self-assembled quantum dots with an electric field applied in the plane of confinement. The interparticle correlations and the carrier distribution are calculated using a configuration interaction approach for dots with circular and square symmetry. We extract universal features of the photoluminescence spectra specific to the lateral coupling configuration and point out the differences with vertically coupled dots. These specific features include additional avoided crossings of the lowest bright exciton level as function of the external field. In the case of strong coupling, the avoided crossing related to exciton dissociation is anomalous and involves an interaction of three or four energy levels. The latter is a consequence of the hole state mixing appearing at the electron transfer between the dots.

Figure 1

(Color online) Top view [cross section $(z=0)$] of the electron confinement potential [Eqs. (1, 2)] for the laterally coupled dots with (a) square or (b) circular disk shape. Colors stand for the depth of the electron confinement (scale given at the right of the figure in meV). The left dot is deeper by $10\mathrm{meV}$.

Figure 2

(Color online) Ground-state exciton energy for a single square quantum dot (the left, deeper one of the model) as function of electric-field orientation for $F=20\mathrm{kV}∕\mathrm{cm}$. The plot contains three double insets. In each inset, left (right) panel shows the contour plot of the electron (hole) density cross section at $z=0$. The square frame shows the nominal dot dimensions of $2a=20\mathrm{nm}$. The arrows indicate the direction of the electric field acting on the electron.

Figure 3

(Color online) Exciton energy spectrum for two coupled square quantum dots. The square quantum dots are put side by side [centers are located at $(-d∕2,0)$ and $(d∕2,0)$] for (a) $d=21\mathrm{nm}$ and (b) $d=20\mathrm{nm}$. Thickness of the lines is proportional to the recombination probability.

Figure 4

(Color online) Electron (left panels, blue) and hole (right panels, red) charge densities for double square quantum dots with $d=21\mathrm{nm}$. Plots (a), (b), (c), and (d) correspond to $F=0,13,47,60\mathrm{kV}∕\mathrm{cm}$, respectively (positive electric field pushes the electron to the right and the hole to the left). The dotted lines show the nominal dot boundaries. The corresponding energy levels marked with the Greek letters are shown in Fig. 3a.

Figure 5

(Color online) Electron (left panels) and hole (right panels) densities for square dots calculated at $F=-40\mathrm{kV}∕\mathrm{cm}$ with a distance between the dot centers of $20\mathrm{nm}$. The dotted lines show the nominal dot boundaries. Corresponding anticrossing energy levels marked by A and B are displayed in Fig. 3b.

Figure 6

Zoom of the rectangle of Fig. 3b for the anomalous ground-state exciton dissociation involving a third energy level in the avoided crossing.

Figure 7

(Color online) Electron (left of each pair of plots) and hole (the right one) densities in four lowest-energy states whose levels were presented in Fig. 6 at $15\mathrm{kV}∕\mathrm{cm}$ (left panel), $17.5\mathrm{kV}∕\mathrm{cm}$ (middle panel), and $20\mathrm{kV}∕\mathrm{cm}$ (right panel). The lower plots correspond to lower energies.

Figure 8

(Color online) Same as Fig. 3 but for circular dots with the dot centers of (a) $d=21\mathrm{nm}$ and (b) $d=20\mathrm{nm}$. The circles mark the avoided crossing discussed in the text.

Figure 9

(Color online) Electron and hole densities for circular dots with distances between the centers of $d=20\mathrm{nm}$ [panels (a)–(c)] and $d=21\mathrm{nm}$ [panel (d)–(f)]. Plots (a)–(c) were calculated at $F_x=-50\mathrm{kV}∕\mathrm{cm}$ and correspond to the hole related avoided crossing marked by a circle in Fig. 8b. Plots (d)–(f) were made for $F_x=70\mathrm{kV}∕\mathrm{cm}$ and correspond to the electron avoided crossing marked by a circle in Fig. 8a. For the hole avoided crossing, the electron density is nearly the same in both participating states (and vice versa). Plots (a), (b), (d), and (f) were made for the lower energy level of the anticrossing couples marked by circles in Fig. 8 and plots (c) and (e) for the higher energy level of each couple.

Figure 10

Energy spectra for electric-field vector of length $F=20\mathrm{kV}∕\mathrm{cm}$ rotated in the $x\text{−}y$ plane [$F_x=F\cos \left(\varphi \right)$, $F_y=F\sin \left(\varphi \right)$] for (a) circular and (b) square dots with centers spaced by $d=20\mathrm{nm}$.

Figure 11

(Color online) Contour plots of the electron (left panels) and hole (right panels) at $z=0$ plane for the square quantum dots at the electric field of $20\mathrm{kV}∕\mathrm{cm}$ oriented at $\varphi =\pi ∕4$ angle. For $\varphi =0$—see Fig. 7—the rightmost column of plots.

Figure 12

(Color online) Spectrum for the square dots with centers separated by $20\mathrm{nm}$ in the $x$ direction and by $10\mathrm{nm}$ in the $y$ direction [see inset in (a)] as (a) function of the field oriented in the $x$ direction and (b) for the field of $F=20\mathrm{kV}∕\mathrm{cm}$ rotated within the plane of confinement.