Continuously tunable dipolar exciton geometry for controlling bosonic quantum phase transitions

The geometry and binding energy of excitons, set by electron-hole wavefunction distributions, are fundamental factors that underpin their many-body interactions and determine optoelectronic properties of semiconductors. However, in typical solid-state systems, these quantities are fixed by material composition and structure. Here we introduce a polarizable interlayer exciton hosted in a two-dimensional tetralayer heterostructure whose dipole length, in-plane radius, and binding energy can be continuously programmed in situ over a wide range, enabling direct control over the nature of excitonic many-body phase transitions. An out-of-plane electric field redistributes layer-hybridized electron-hole wavefunctions, realizing in situ control of exciton geometry through a strong quadratic Stark response. This tunability further regulates the nature of interaction-driven Mott transition, transforming it from gradual to abrupt. Our results establish exciton geometry as a continuously tunable materials parameter, opening routes to exciton-based quantum phase-transition simulators and guiding the design of emergent optoelectronic functionalities from programmable excitonic materials.

💡 Research Summary

In this work the authors demonstrate a novel platform for continuously tuning the geometry of interlayer excitons (IXs) in a two‑dimensional tetralayer transition‑metal dichalcogenide (TMD) heterostructure. By stacking a bilayer of WSe₂ on top of a bilayer of WS₂ with a small twist angle (R‑stacked configuration) and embedding the stack between graphite top and bottom gates, they apply a vertical electric field (E z) that redistributes the layer‑hybridized electron and hole wavefunctions. Because the conduction‑band minimum resides in WS₂ and the valence‑band maximum in WSe₂, the electron and hole are not confined to a single layer; instead their probability density spreads over several layers and shifts with the applied field. This field‑driven redistribution simultaneously changes the exciton dipole length (d), the in‑plane Bohr radius (a*), and the binding energy (E_b).

Photoluminescence (PL) and reflectance‑contrast (RC) measurements reveal a pronounced quadratic Stark shift of the IX emission energy, ΔE = −ed E z − αE z², where the second‑order coefficient α≈6.8 eV·nm²·V⁻² is among the largest reported for 2D dipolar excitons. The extracted dipole moment can be tuned from ≈0.57 e·nm at positive fields to ≈1.54 e·nm at −120 mV nm⁻¹, a threefold variation that far exceeds the fixed ≈0.6 e·nm value of conventional WSe₂/WS₂ bilayers. Density‑dependent PL linewidth analysis shows that, as the dipole length and a* increase, the critical density for the exciton Mott transition (n_M) shifts to lower values and the transition width Δn narrows dramatically. In other words, large, loosely bound IXs undergo an almost abrupt Mott ionization, whereas compact IXs display a gradual crossover. This continuous, field‑controlled evolution reconciles previously contradictory reports of both gradual and abrupt Mott transitions in 2D semiconductors, identifying exciton geometry and binding energy as the decisive parameters.

Control experiments on H‑stacked (180° twisted) bilayers, which forbid interlayer hybridization due to opposite valley‑spin alignment, exhibit only linear Stark shifts and discrete dipole configurations, confirming that the continuous tunability originates from valley‑spin‑allowed hybridization in the R‑stacked tetralayer. Density functional theory calculations corroborate the experimental findings, showing strong layer mixing at the K‑valley band edges for the R‑stacked homo‑bilayers and negligible mixing for the H‑stacked case.

Overall, the paper establishes three key advances: (i) a continuously programmable exciton dipole and in‑plane size via an external electric field, (ii) a record‑high exciton polarizability enabling large‑amplitude dipole modulation, and (iii) a geometry‑driven tuning of the many‑body Mott transition from gradual to abrupt. These results open a pathway toward exciton‑based quantum simulators, electrically reconfigurable optoelectronic devices, and the broader concept of “programmable excitonic materials” where fundamental quasiparticle properties can be dialed in situ.