Superlattice Quantum Solid of Dipolar Excitons

We study dipolar excitons confined at 330 mK in a square electrostatic lattice of a GaAs double quantum well. In the dipolar occupation blockade regime, at $3/2$ filling, we evidence that excitons form a face-centered superlattice quantum solid. This phase is realized with high purity across 36 lattice sites, in a regime where the mean interaction energy exceeds the depth of the electrostatic lattice confinement. The superlattice solid then closely relates to Wigner crystals.

Figure 1

(a) A MI at $\overline{\nu }=1$ (red balls in gray waves) imprints a dipolar potential (violet area) larger than the confinement depth. Enlargement: excitons all lie at the same $4V_E$ energy due to four intralattice NN repulsions. (b) Excitons (blue balls) confined in the dipolar lattice (red wave) induced by the MI. Enlargement: exciton energies in the electrostatic potential are given by the number of interlattice interactions with strength $V_{E,D}$ (bottom right). Intralattice interactions ($V_D$) control accessible energies in the dipolar lattice (top right). (c) PL spectrum radiated by a MI at unity filling, together with the profile of our spectral response function (red area). The profile is adjusted (solid black line) by the sole line (0). (d) PL spectrum at $\overline{\nu }=1.2$. The profile is adjusted (solid black line) by setting the fractions of interlattice NN interactions (red areas for each number of NN—0 to 4—at energies given by vertical lines) and the occupation of WS1 (I) and WS2 (III) (blue areas). In (c) and (d), insets show the occupation fraction of each accessible state. PL spectra are obtained by averaging across 36 lattice sites; error bars display our statistical precision.

Figure 2

(a) Top panel: sketch of the superlattice quantum solid made by a CB in the dipolar lattice (blue) and a MI in the electrostatic one (red) across 36 sites. The violet square represents the elementary superlattice cell. Middle panel: spatially and spectrally resolved PL at $\overline{\nu }=3/2$. Bottom panel: disordered arrangement in the dipolar lattice around half-filling with stripes and CB patterns. (b) PL spectrum emitted at the center of the illuminated region [C in panel (a)], together with the theoretical spectrum for a superlattice quantum solid (purple shaded area). (c) PL spectrum measured in region S of panel (a). In (b),(c) PL spectra are averaged over 36 sites and model profiles (black lines) are obtained by adjusting the contributions from interlattice NN interactions (red bars in inset), and WS occupations together with NN interactions in the dipolar lattice (blue bars in inset). The insets in (b) and (c) show the occupation fractions of accessible states. (d),(e) Vertically resolved exciton compressibility, averaged across 36 sites, in the electrostatic (d) and dipolar (e) lattices, together with the profile of the PL intensity (gray shaded area). In (b)–(e) error bars display our statistical precision.

Figure 3

(a) A single exciton in a dipolar lattice site (blue) shifts the energies of NN excitons in the electrostatic potential (red) by $V_{E,D}$. (b) Exciton compressibility in the electrostatic lattice as a function of the fraction of sites with at least 1 NN in the dipolar lattice. When this observable reaches 0.85 we estimate that $\overline{\nu }\sim 1.2$. (c) The interaction potential created by excess excitons in the dipolar lattice (green area) dresses the electrostatic lattice confinement. Its depth is surpassed at $\overline{\nu }\gtrsim 4/3$. (d) Compressibilities ${\kappa }_E$ (red) and ${\kappa }_D$ (blue) as a function of the total filling fraction $\overline{\nu }$ where SLI refers to superlattice insulator. In (b) and (d) measurements are all averaged across 50 lattice sites. Error bars display our statistical precision, while lines are guides for the eye.