A Gross-Pitaevskii theory for an excitonic incompressible Bose solid

Abstract

We show that interlayer excitons in double-layer semiconductor heterostructures can form a Bose solid, which is an incompressible supersolid characterized by exactly one boson per lattice site. This exciton Bose solid would be the first realization of an incompressible supersolid, unlike the generally compressible cluster supersolids seen in dipolar quantum gases. Capturing its characteristics and associated emergent phenomena requires extending the Gross-Pitaevskii formalism to include strong two-particle correlations and exclude exciton self-interactions. We develop such a formalism, we apply it across experimentally accessible exciton densities and interlayer separations, and we show that it incorporates both superfluid and incompressible supersolid ground states. This extended framework allows us to determine the superfluid-supersolid transition and explore the low-temperature properties of the exciton supersolid across its complete parameter space.

Figures (3)

• Figure 1: Profile along diagonal and the spatial distribution of order parameter $|\Psi(\mathbf{r})|^2$ for $r_0=30$. Panels (a)--(d) correspond to the interlayer separations $d=1,7,15,20$, respectively. Shaded area shows the homogeneous background component of $|\Psi(\mathbf{r})|^2$.
• Figure 2: (a) Dependence on interlayer separation $d$ of $\rho_{B}/\rho$, the amplitude of the homogeneous background component of $\Psi(\mathbf{r})$, for $r_0=30$. (b) Energy eigenvalue of the supersolid state (SS) and corresponding eigenvalue of the superfluid state (SF), calculated without the self-interaction correction.
• Figure 3: The phase diagram at zero temperature, as a function of interlayer separation $d$ and average interparticle spacing $r_0$. Dashed red line: superfluid to supersolid transition. Dash-dotted grey line: Superfluid and supersolid condensate collapse into a normal electron-hole liquid Pascucci2025note. Dashed green line: exciton liquid to normal exciton solid transition taken from Ref. Astrakharchik2007. Dotted black line: $d=r_0$. Insets: order parameter profile $|\Psi(\mathbf{r})|^2$ at the points indicated by grey dots.