Micropatterned electrostatic traps for indirect excitons in coupled GaAs quantum wells

We demonstrate an electrostatic trap for indirect excitons in a field-effect structure based on coupled GaAs quantum wells. Within the plane of a double quantum well, indirect excitons are trapped at the perimeter of a $\mathrm{Si}{\mathrm{O}}_2$ area sandwiched between the surface of the GaAs heterostructure and a semitransparent metallic top gate. The trapping mechanism is well explained by a combination of the quantum confined Stark effect and local field enhancement. We find the one-dimensional trapping potentials in the quantum well plane to be nearly harmonic with high spring constants exceeding $10\mathrm{keV}∕{\mathrm{cm}}^2$.

Figure 1

(Color online) (a) Schematic side view and (b) top view of the field-effect structure with an additional $\mathrm{Si}{\mathrm{O}}_2$ layer on top of the $\mathrm{Ga}\mathrm{As}∕\mathrm{Al}\mathrm{Ga}\mathrm{As}$ heterostructure. Long-living excitons are laser generated in the coupled quantum wells (QWs). By appropriately tuning the bias $V_B$ and the control voltage $V_C$ with respect to the back gate, excitons can be captured and stored along the perimeter of $\mathrm{Si}{\mathrm{O}}_2$ layers with varying curvature, as shown in (c). The intensity of the photoluminescence is color coded, while the bias voltage is set to be $V_B=0\mathrm{V}$ and the control gate floats.

Figure 2

(Color online) Excitonic photoluminescence emitted from an electrostatic, circular trap at $T=3.7\mathrm{K}$. After the excitons have been generated by a pulsed laser approximately $50\mu \mathrm{m}$ away from the circular trap, they diffuse into the trap and recombine. The trap can be electrically switched from (a) “on” to (b) “off” by voltage $V_C$, while voltage $V_B$ is kept constant at $0\mathrm{V}$. The dashed circle depicts the perimeter of the circular $\mathrm{Si}{\mathrm{O}}_2$ layer with a diameter of $160\mu \mathrm{m}$. By using a bandpass filter, we ensure that only the photoluminescence of indirect excitons is recorded. (c) Time-integrated photoluminescence on top of the bias gate at a voltage of $V_B=0\mathrm{V}$ without a filter, showing both direct and indirect (arrow) excitons. (d) The equivalent measurement on top of the control gate exhibits only direct excitons. See text for details.

Figure 3

(Color online) Switching characteristics of the circular trap. (a) At a constant bias voltage of $V_B=+0.3\mathrm{V}$, the circular excitonic photoluminescence pattern is detected for $V_C<0.48\mathrm{V}$. The solid curve is a guide to the eyes. (b) Phase diagram of the trapping behavior in the $V_C-V_B$ space. The dashed line refers to the data shown in (a).

Figure 4

(Color online) (a) Electrostatic potential $\phi \left(\mathit{r}\right)$ (color coded) at the perimeter of the $\mathrm{Si}{\mathrm{O}}_2$ layer (see inset on the top) for $V_{\mathrm{I}}=0\mathrm{V}$, $V_{\mathrm{II}}=-0.4\mathrm{V}$, and $V_{\mathrm{III}}=-0.78\mathrm{V}$. The thin curves indicate equipotential lines of the electrostatic potential. (b) Calculated excitonic energy $\Delta U_{\mathit{exc}}$ due to the quantum confined Stark effect in the region indicated by the dashed rectangle in (a). The voltage $V_{\mathrm{II}}$, swept in steps of 0.1 V, is indicated at each associated curve. The position $x=0$ corresponds to the boundary between regions II and III, where a minimum of excitonic energy is found. Inset: increasing the voltage $V_{\mathrm{II}}$ above approximately $-0.6\mathrm{V}$ induces lateral electric field components $E_{\mathrm{lat}}$, which eventually give rise to exciton ionization.

Figure 5

(Color online) Excitonic recombination energy $U_{\mathit{exc}}$ as a function of the position $x$. The excitons are trapped a few microns away from the perimeter of the $\mathrm{Si}{\mathrm{O}}_2$ layer at $T=3.7\mathrm{K}$ [see schematic top view in the inset of (b)]. The spring constants $k$ of the trapping potentials shown in (a) and (b) are obtained by numerically fitting harmonic functions (solid curves) to the measured data.

Figure 6

(Color online) (a) Predicted excitonic energies in coupled quantum wells located $30\mathrm{nm}$ below a surface stressor. Here, the exciton trapping is expected to be anisotropic because boundaries of the stressor facing the [110] direction give rise to exciton energies lower than the ones in the $[-110]$ direction. (b) Measured photoluminescence emission of a circular trap at $T=3.7\mathrm{K}$. Strain effects can be excluded as a dominant effect for trapping since the photoluminescence is isotropic along the boundaries of the $\mathrm{Si}{\mathrm{O}}_2$ layer.