Strain-induced active tuning of the coherent tunneling in quantum dot molecules

We demonstrate experimentally the possibility to manipulate the coupling strength in an asymmetric pair of electronically coupled InGaAs quantum dots by using externally induced strain fields. The coupling strength of holes confined in the dots increases linearly with increasing tensile strain. A model based on $\mathit{k}·\mathit{p}$ theory explains the effect in terms of modified weight of the light hole component mediating the coupling in the barrier. Our results are relevant to the creation and control of entangled states in optically active quantum dots.

Figure 1

(a) Sketch of the device. Vertically stacked, disk-shaped InGaAs QDs (bottom-B/top-T QD with a nominal height of 2.9/3.3 nm and a spacer thickness of 5.4 nm) are embedded in n-i-p nanomembranes integrated on top of a piezoelectric actuator (PMN-PT) allowing in situ application of biaxial stresses by tuning the voltage (electric field) $V_p$ ($F_p$). Independently, a voltage $V_d$ applied to the nanomembranes allows the electric field ($F_d$) across the QDs to be controlled. (b) Color-coded microphotoluminescence ($\mu$PL) maps of a representative QDM as a function of $F_p$ and $F_d$ (PL intensity in logarithmic scale). The typical anticrossings observed (${\mathrm{AC}}_{1–4}$) are associated with hole tunneling and are marked on the map at $F_p=0$ kV/cm. (c) Sketch of the transition energies of the positively charged ($X^{+}$) and neutral ($X^0$) excitons in a QDM (the $X^{+}$ pattern is obtained by the formula reported in the Supplemental Material [37]). By sweeping $F_d$, different transitions are defined: two direct (${}_{\underline{2}0}^{\underline{1}0}{X}^{+}$ and ${}_{\underline{1}1}^{\underline{1}0}{X}^{+}$) and two indirect (${}_{1\underline{1}}^{\underline{1}0}{X}^{+}$ and ${}_{2\underline{0}}^{\underline{1}0}{X}^{+}$) with a larger Stark shift. The two additional lines are direct recombinations arising from the neutral exciton (${}_{\underline{1}0}^{\underline{1}0}{X}^0$) and the doubly positively charged exciton (${}_{\underline{2}1}^{\underline{1}0}{X}^{2+}$).

Figure 2

Color-coded $\mu$PL maps of the (a), (b) ${\mathrm{AC}}_1$ and (c), (d) ${\mathrm{AC}}_2$ regions as a function of $F_d$ at $F_p=20$ kV/cm (compressive strain, $-$0.04%) and $F_p=-10$ kV/cm (tensile strain, 0.02%), respectively. The dashed line marks the AC position. (e) Parabolic behavior of the energy splitting ($\Delta E$) between the bonding and antibonding molecular states around ${\mathrm{AC}}_1$ as a function of $F_d$ at $F_p=20$, 10, 0, $-$10 kV/cm. (f) Behavior of $\Delta$$E_{\mathrm{AC}}$ at ${\mathrm{AC}}_{1–4}$ as a function of the neutral exciton PL energy shift ($\Delta E_p$), when $F_p$ is varied through the whole tuning range ($\Delta F_p=30$ kV/cm). (g) $\Delta E_{\mathrm{AC}}$ and the tuning range of the coupling strength in the range $F_p=20$ to $-$10 kV/cm for six QDMs.

Figure 3

(a) Color-coded $\mu$PL map of a representative QDM as a function of $F_d$ at $F_p=-10$ kV/cm. (b) Transition energies of $X^{+}$ in the QDM (AC lines) resulting from a fit to the experimental spectrum of (a). All the parameters used to fit the data are listed in Table S1 [37]. (c) Tunneling energies of single hole ($t_h$) and $X^{+}$ ($t_{X^{+}}$) and electron-hole exchange interaction ($J_{eh}$) as a function of $\Delta E_p$, when $F_p$ is varied in the whole range. (d) Three-dimensional hole probability density of light hole (LH, green) and heavy hole (HH, red) in the QDM (gray). The center-to-center dot separation is 8.5 nm. (e) Confinement potentials of LH (green) and HH (red) for the structure without (solid) and with induced compressive strain of ${\epsilon }_{xx}={\epsilon }_{yy}=-0.1\%$ (dotted). Energy is displayed in the electron view. (f) Hole probability density in the barrier region of LH (green), HH (red), and total (black) for the unstrained (solid) and strained (dotted) case.