Gate controlled Aharonov-Bohm-type oscillations from single neutral excitons in quantum rings

We report on a magnetophotoluminescence study of single self-assembled semiconductor nanorings which are fabricated by molecular-beam epitaxy combined with ${\text{AsBr}}_3$ in situ etching. Oscillations in the neutral exciton radiative recombination energy and in the emission intensity are observed under an applied magnetic field. Further, we control the period of the oscillations with a gate potential that modifies the exciton confinement. We infer from the experimental results, combined with calculations, that the exciton Aharonov-Bohm effect may account for the observed effects.

Figure 1

(Color online) (a) AFM image of the QRs shown together with a cross-sectional TEM image of a single QR. PL spectrum of a single QR (with a nominal etching depth of 3 nm) is shown in the right. The inset presents the structure parameters. [(b) and (c)] Color-coded maps of the logarithm of the PL intensity as a function of magnetic field and PL energy. For comparison, data for a single QD are shown in (c).

Figure 2

(Color online) PL energy is tuned by quantum confined Stark effect at small voltage steps. The upper figure shows a large tuning range of $120\mu \text{eV}$ while the lower figure shows a smaller tuning range with much smaller voltage steps. The fit peak positions, with error of $\pm 1.5\mu \text{eV}$, fall well into the 95% prediction band of the fit function.

Figure 3

(Color online) Linear polarization-dependent energy shift of X and XX. The solid lines are sine wave fittings.

Figure 4

(Color online) Fitted PL peak position versus $B$ field after averaging the Zeeman splitting for (a) a QR and (b) a QD neutral exciton emission. The lines are the quadratic fits. Oscillations in PL energy for the 3 nm etched QR and corresponding normalized PL intensity as a function of $B$ field are shown in (c) and (e), respectively. The solid lines represent the smoothed data using a Savitzky-Golay filter. For a reference QD, (d) the neutral exciton shows no energy oscillation within an error region of $\pm 2.5\mu \text{eV}$ (gray area) and (f) also the normalized PL intensity shows no clear quenching.

Figure 5

(Color online) Schematic of the gated QR structure. (b) Under a forward bias of 2.8 V the emission energy shows clear transitions at 2.6 and 8 T (upper part, the solid line represents the Savitzky-Golay smoothed data and is used as guide to the eye). When the bias changes from 2.8 to 0.8 V, the transitions shift smoothly (lower part) to higher magnetic fields. (c) Color-coded maps of the PL intensity as a function of magnetic field and external bias.

Figure 6

(Color online) (a) Second derivative of the exciton energy of the state with $L=0$. Calculations are shown for four different values of the electric field. (b) The effective radius of the electron and the hole, defined as ${\int {\Psi }_L^{\ast }\left({\vec{r}}_e,{\vec{r}}_h\right){\rho }_{e\left(h\right)}{\Psi }_L\left({\vec{r}}_e,{\vec{r}}_h\right)d{\vec{r}}_{e}d\vec{r}}_h$. (c) The radius ${\lambda }_{ex}={\left[\left(m_h+m_e\right)/\left(m_h/{⟨{\rho }_e⟩}^2+m_e/{⟨{\rho }_h⟩}^2\right)\right]}^{0.5}$, which corresponds to the exciton radius definition for a 3D system. (d) The diamagnetic coefficient ${\gamma }_2$ changes with applied bias. (e) The binding energies of XX and ${\text{X}}^{+}$ change by nearly the same amount with external $E$ field.

Figure 7

(Color online) Charge-neutral and positively charged exciton complexes show similar peak energy oscillations. The data are given at $V=1.8$ and 1.0 V. The solid line represents the smoothed data and is used as guide to the eye.

Figure 8

(Color online) PL intensity for the (a) charge-neutral and (b) positively charged exciton complexes plotted versus $B$ field at several different bias. The solid lines mark the general shift of the PL intensity with increasing bias.