Abstract
Strongly interacting electronic systems often exhibit a complicated phase diagram that results from the competition between different quantum ground states. One feature of these phase diagrams is the emergence of microemulsion phases, where regions of different phases self-organize across multiple length scales. The experimental characterization of these microemulsions can pose considerable challenges, as the long-range Coulomb interaction microscopically mingles with the competing states. Here we observe the signatures of the microemulsion between an electronic Wigner crystal and an electron liquid in a MoSe2 monolayer using cryogenic reflectance and magneto-optical spectroscopy. We find that the transition into this microemulsion state is marked by anomalies in exciton reflectance, spin susceptibility and umklapp scattering, establishing it as a distinct phase of electronic matter.
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Acknowledgements
We acknowledge useful discussions with S. Kivelson, S. Das Sarma, A. Imamoglu, T. Smolenski, N. Leisgang and A. A. Zibrov. We thank T. Smolenski for sharing some of his unpublished data with us. We acknowledge support from AFOSR (FA9550-21-1-0216), the DoD Vannevar Bush Faculty Fellowship (N00014-16-1-2825 for H.P. and N00014-18-1-2877 for P.K.), NSF CUA (PHY-1125846 for H.P., E.D. and M.D.L.), Samsung Electronics (for H.P. and P.K.), NSF (PHY-1506284 for H.P. and M.D.L. and DGE-1745303 for E.B.), AFOSR MURI (FA9550-17-1-0002), ARL (W911NF1520067 for H.P. and M.D.L.) and DOE (DE-SC0020115 for H.P. and M.D.L. and DE-SC0022885 for Y.Z.). E.D. acknowledges support by the SNSF project no. 200021_212899. K.W. and T.T. acknowledge support from the JSPS KAKENHI (grant nos 19H05790, 20H00354 and 21H05233). The Flatiron Institute is a division of the Simons Foundation.
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H.P. and E.D. conceived the project. J.S., J.W., G.S., Y.Z. and E.B. fabricated the samples and designed and performed the experiments. I.E. and P.A.V. performed calculations. I.E., P.A.V., Y.Y., M.A.M., S.Z., A.J.M. and E.D. contributed to theoretical descriptions. J.S., J.W., I.E. and P.A.V analysed the data. T.T. and K.W. provided hBN samples. J.S., J.W., I.E., P.A.V., E.D. and H.P. wrote the paper with extensive input from the other authors. H.P., E.D., P.K. and M.D.L. supervised the project.
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Extended data
Extended Data Fig. 1 Optical image of device 1 and device 2.
a-b, Optical microscope image of (a) device D1 and (b) device D2. The MoSe2 monolayer regions are indicated by white dashed lines, and the solid red lines show the outline of the bottom gate electrode: (a) Pd/Au metal and (b) a few-layer graphite.
Extended Data Fig. 2 Umklapp features in another spot in the original device, D1, and in another device, D2.
Color map of the derivative of reflectance contrast spectra with respect to electron density at a base lattice temperature of 16 mK. A Lorentzian fitted exciton/RP peak was subtracted to emphasize the Umklapp features. The green line represents the fitted exciton/RP resonance energy, and the black dashed line indicates the expected resonance energy from umklapp scattering of excitons. Umklapp features in D1 (another spot from that shown in main Fig. 1) and in another device, D2, are shown in (a) and (b), respectively. Color map of the derivative of reflectance contrast spectra with respect to electron density, without subtracting the fitted exciton/RP Lorentzian in another spot in D1 (c) and in another device D2 (d).
Extended Data Fig. 3 Electron temperature estimation at low density under different incident light powers.
a-d, We plot the signal \(\widetilde{M}\) at the electron density of 0.30×1012 cm-2 under varying light powers: (a) 60 fW, (b) 320 fW, (c) 3.3 pW, and (d) 32 pW. From a fit using the Brillouin function, we estimate the electron temperature. The estimated electron temperatures are: (a) 80 mK, (b) 130 mK, (c) 180 mK, and (d) 350 mK.
Extended Data Fig. 4 Anomalies in the main excitonic properties.
a, Near the density of \({n}_{* }\) = 0.9×1012 cm-2, a noticeable discontinuity in the derivative of the exciton/RP resonance energy with respect to electron density, \(d{E}_{X}/{dn}\) is observed, signifying a change in the slope of the exciton/RP resonance energy. b, A pronounced slope change of the oscillator strength is observed near the density of \({n}_{* }\) = 0.9×1012 cm-2. Reflectance contrast spectra measurements were performed under a light power of 0.7 nW at a base lattice temperature of 16 mK. The black arrows on the top x-axis and black dashed lines indicate the characteristic densities, \({n}_{{\rm{WC}}}\) and \({n}_{* }\). Linear decrease of the oscillator strength upon doping is represented by the grey dashed line. The measured excitonic properties are a convolution of the intrinsic properties of its electronic environment and the details of how the exciton couples to the electrons. In particular, the exciton is sensitive to the electronic compressibility. Non-analytic behavior of the compressibility at the microemulsion-liquid transition should therefore be expected to lead to rapid changes in the excitonic properties.
Extended Data Fig. 5 Reduced spin susceptibility as a function of electron density at different temperatures.
a-f, The Curie susceptibilities in the Wigner crystal regime are indicated by grey dashed lines. The spin susceptibility between \({n}_{{\rm{WC}}}\) and \({n}_{* }\) aligns well with the colored dashed lines, representing intermediate density ranges that follow the lever rule. However, notable deviations from this linear behavior are observed in the vicinity of \({n}_{{\rm{WC}}}\) and \({n}_{* }\), signifying interface effects between the crystal and liquid regions. The boundaries of these density ranges are delineated by black vertical dashed lines, with these regions further emphasized by black arrows. The density ranges are quantified by the error bars in Fig. 4 of the main text. The determination of the transition near \({n}_{* }\) and the density ranges are described in Fig. S19.
Extended Data Fig. 6 Magnetic field dependence of n*.
a, Derivative of fitted exciton/RP resonance energy with respect to electron density for left circularly polarized reflectance contrast at various magnetic fields. The black dotted line marks the electron density (\({n}_{* }\)) that corresponds to the center of the jump in \(d{E}_{X}/{dn}\) at 9 T. b, Color maps showing left circularly polarized differential reflectance contrast are plotted as a function of electron density at various magnetic fields. The white dotted line marks the electron density at which the discontinuity (\({n}_{* }\)) occurs at 9 T.
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Sung, J., Wang, J., Esterlis, I. et al. An electronic microemulsion phase emerging from a quantum crystal-to-liquid transition. Nat. Phys. 21, 437–443 (2025). https://doi.org/10.1038/s41567-024-02759-8
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DOI: https://doi.org/10.1038/s41567-024-02759-8
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