Giant permanent dipole moment of two-dimensional excitons bound to a single stacking fault

We investigate the magneto-optical properties of excitons bound to single stacking faults in high-purity GaAs. We find that the two-dimensional stacking fault potential binds an exciton composed of an electron and a heavy hole, and we confirm a vanishing in-plane hole $g$-factor, consistent with the atomic-scale symmetry of the system. The unprecedented homogeneity of the stacking-fault potential leads to ultranarrow photoluminescence emission lines (with a full width at half-maximum $\lesssim 80\mu \text{eV}$) and reveals a large magnetic nonreciprocity effect that originates from the magneto-Stark effect for mobile excitons. These measurements unambiguously determine the direction and magnitude of the giant electric dipole moment $\left(\gtrsim e\times 10\text{nm}\right)$ of the stacking-fault exciton, making stacking faults a promising new platform to study interacting excitonic gases.

Figure 1

(a) Confocal scan of SF structures. The image is formed by coloring emission in different wavelength bands as red, blue, or green, as depicted in (e). Excitation at 1.53 eV, $100\mu \mathrm{W}$, and 1.9 K excite and collect $H$ polarization [see (b)]. (b) Diagram of SF pyramid. The up, down, left, and right SFs are labeled, along with the $H$ and $V$ polarizations. (c) Comparison of perfect zinc-blende and stacking fault crystal structure. (d) Detail of SF pyramid structure. Excitation at 1.53 eV, $100\mu \mathrm{W}$, 1.7 K. (e) Low-power PL spectra at colored dots in (d). Polarizations: blue, excite and collect $H$; green and red, excite and collect $V$. Broadband luminescence is observed from the SF edges (red); 1.53 eV, 2 $\mu \mathrm{W}$, and 1.7 K. (f) PL from down SF [blue dot in (d)]. Polarizations: dark blue, excite and collect $H$; light blue, excite and collect $V$.

Figure 2

(a) Spectra from up and down SFs as a function of in-plane magnetic field. The spectra show a nonreciprocity with applied magnetic field. Excite at 1.65 eV, 0.5 $\mu \mathrm{W}$, 1.6 K, excite and collect $H$. The inset shows the geometry of the stacking fault pyramid and applied magnetic field. (b) Spectra from left and right SFs as a function of partially out-of-plane magnetic field. The spectra are similar at positive and negative fields. Excitation at 1.65 eV, 0.5 $\mu \mathrm{W}$, 1.6 K, excite and collect V.

Figure 3

(a) Because of the conservation of in-plane momentum during exciton recombination, the angle of light emission depends on the exciton wave vector. Collecting different angles probes different exciton momenta. The SF has a built-in potential that creates a zero-field dipole moment for the SF exciton. In the exciton frame of reference, the in-plane magnetic field becomes an out-of-plane electric field, leading to the magneto-Stark effect. (b) Spectra of up and down SFs as a function of $\theta$ and in-plane magnetic field $B_y$. (c) Light from the up SF originates from excitons with larger $K_x$ than light from the down SF (for $\theta >0$). (d) and (e) Spectra of up and down SF at positive and negative $B_y$ for $\theta =0^{\circ }$ and ${43}^{\circ }$. At $\theta =0^{\circ }, \mathrm{\Delta }{E}_{\text{up}}$ and $\mathrm{\Delta }{E}_{\text{down}}$ have the same magnitude, while for $\theta ={43}^{\circ }$, the magnitude of $\mathrm{\Delta }{E}_{\text{up}}$ is larger than that of $\mathrm{\Delta }{E}_{\text{down}}$. (f) and (g) Splitting $\mathrm{\Delta }{E}_{\text{up/down}}$ as a function of magnetic field. Data are obtained from Voigt fits to spectra similar to those shown in (d) and (e). Solid lines are a fit to $\mathrm{\Delta }E=aB$ for the first three data points. (h) The ratio of $B=0$ slopes, Eq. (6), depends only on geometrical constraints. The theory (solid line) has no adjustable parameters. Data for other angles in Ref. [21].