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Dual-density waves with neutral and charged dipolar excitons of GaAs bilayers


Strongly correlated quantum particles in lattice potentials are the building blocks for a wide variety of quantum insulators—for instance, Mott phases and density waves breaking lattice symmetry1,2,3. Such collective states are accessible to bosonic and fermionic systems2,4,5,6,7,8,9,10,11,12. To expand further the spectrum of accessible quantum matter phases, mixing both species is theoretically appealing because density order then competes with phase separation13,14,15,16. Here we manipulate such a Bose–Fermi mixture by confining neutral (boson-like) and charged (fermion-like) dipolar excitons in an artificial square lattice of a GaAs bilayer. At unitary lattice filling, strong inter- and intraspecies interactions stabilize insulating phases when the fraction of charged excitons is around (1/3, 1/2, 2/3). We evidence that dual Bose–Fermi density waves are then realized, with species ordered in alternating stripes. Our observations highlight that dipolar excitons allow for controlled implementations of Bose–Fermi Hubbard models extended by off-site interactions.

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Fig. 1: Neutral and charged excitons’ Bose–Fermi mixture.
Fig. 2: Charged exciton insulators at unity and half fillings.
Fig. 3: Dual-density waves of neutral and charged excitons.

Data availability

Source data are available for download, together with the published manuscript.


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Research at CNRS (C.L. and F.D.) has been financially supported by IXTASE from the French Agency for Research (no. ANR-20-CE30-0032-01). The work at Princeton University (L.P. and K.B.) was funded in part by the Gordon and Betty Moore Foundation’s EPiQS Initiative (grant no. GBMF9615 to L.P.) and by the National Science Foundation MRSEC (grant no. DMR 2011750) to Princeton University.

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Authors and Affiliations



K.B. and L.P. realized the GaAs bilayer while C.L., S.S. and F.D. fabricated the gate electrodes imprinting the 250-nm-period electrostatic lattice. C.L. and F.D. performed all experiments and data analysis and wrote the manuscript. F.D. designed the project.

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Correspondence to François Dubin.

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Nature Materials thanks David Ruiz-Tijerina and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Lattice filling vs. gate voltage.

a Total integrated intensities of the PL radiated by neutral and charged excitons, as a function of Vg and at unitary filling (P=14 nW). b Same experimental results as in a but expressed as a function of νCX. c Scaling of νCX as a function of Vg deduced from the measurements shown in a and b. The line provides a guide for the eyes. Experiments were all realised at 330 mK and acquired during four different experimental runs so that detection efficiencies are close but not identical. Vertical error bars display the poissonian precision in a-b and the ± 0.03 precision on νCX in c. In a-c, the horizontal error is smaller than the points size while in b it corresponds to the precision when extracting νCX.

Source data

Extended Data Fig. 2 Evaluation of the residual doping level.

PL spectrum radiated by neutral dipolar excitons for νX ≈ 1/2 (at νCX ≈ 0). The spectrum is measured by averaging 10 realisations performed under unchanged conditions. The profile is given by our spectral resolution, that is reproduced by a single lorentzian-like line with around 150 μeV full-width-at-half-maximum (blue area and black line). Measurements were performed at 330 mK, error bars displaying the level of poissonian fluctuations.

Source data

Extended Data Fig. 3 Thermal melting of CX insulators at νCX = 1/2 and 1.

a Compressibility κCX normalised to the level given by poissonian noise for (νCX = 1/2, νX ≈ 0) as a function of the bath temperature. b Identical measurements for (νCX = 1, νX ≈ 0) . While in a the thermal melting of the insulating phase occurs around 1K, as expected for the magnitude measured for VCX,CX, a similar critical temperature is found in b for the Mott phase. This possibly reflects fluctuations of the density of injected holes while the bath temperature is increased. For all measurements error bars mark our statistical precision when computing the compressibility ( ± 0.03).

Source data

Extended Data Fig. 4 Interaction energies and spatial ordering.

Possible configurations of incompressible phases made by neutral (blue) and charged (red) excitons. The respective energy shifts of PL energies, EX and ECX, are indicated below each configuration together with the resulting magnitude of ΔEX,CX, by only taking into account NN interactions.

Source data

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Lagoin, C., Suffit, S., Baldwin, K. et al. Dual-density waves with neutral and charged dipolar excitons of GaAs bilayers. Nat. Mater. 22, 170–174 (2023).

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