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Competing correlated states around the zero-field Wigner crystallization transition of electrons in two dimensions


The competition between kinetic energy and Coulomb interactions in electronic systems leads to complex many-body ground states with competing orders. Here we present zinc oxide-based two-dimensional electron systems as a high-mobility system to study the low-temperature phases of strongly interacting electrons. An analysis of the electronic transport provides evidence for competing correlated metallic and insulating states with varying degrees of spin polarization. Some features bear quantitative resemblance to quantum Monte Carlo simulation results, including the transition point from the paramagnetic Fermi liquid to Wigner crystal and the absence of a Stoner transition. At very low temperatures, we resolve a non-monotonic spin polarizability of electrons across the phase transition, pointing towards a low spin phase of electrons, and a two-order-of-magnitude positive magnetoresistance that is challenging to understand within traditional metallic transport paradigms. This work establishes zinc oxide as a platform for studying strongly correlated electrons in two dimensions.

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Fig. 1: The device and quantum transport.
Fig. 2: The metal–insulator transition.
Fig. 3: Spin polarization in an in-plane magnetic field.
Fig. 4: Nonlinear transport characteristics and phase diagram.

Data availability

The data that support the findings of this study are available from the corresponding author on request.


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We appreciate discussions with I. Aleiner, J. Checkelsky, S. Das Sarma, N. Drummond, J. Eisenstein, S. Kivelson, C. Murthy, B. Narozhny, B. Spivak and A. Young, along with technical support from J.-S. Xia, N. Sullivan, G. Euchner and S. Wahl. J.F. acknowledges support from the Max Planck Institute, University of British Columbia and University of Tokyo Center for Quantum Materials; the Deutsche Forschungsgemeinschaft (FA 1392/2-1); and the Institute for Quantum Information and Matter, a National Science Foundation Physics Frontiers Center (grant PHY-1733907). B.S. acknowledges support from the National Science Foundation under grant DMR-2045742. Y.K. acknowledges the Japan Science and Technology Agency, PRESTO grant number JPMJPR1763, Japan. M.K. acknowledges the financial support of the Japan Science and Technology Agency, CREST grant number JPMJCR16F1, Japan.

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Authors and Affiliations



J.F. and D.T. gathered experimental data. J.F. performed the molecular beam epitaxy with assistance from Y.K., A.T. and M.K. J.F., I.S. and B.S. wrote the manuscript. All authors discussed the results and commented on the manuscript.

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Correspondence to J. Falson.

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The authors declare no competing interests.

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Peer review information Nature Materials thanks Rui-Rui Du, Raymond Ashoori and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary Figs. 1–15, Table 1 and Discussion.

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Falson, J., Sodemann, I., Skinner, B. et al. Competing correlated states around the zero-field Wigner crystallization transition of electrons in two dimensions. Nat. Mater. 21, 311–316 (2022).

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