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Interaction-Driven Quantum Phase Transitions between Topological and Crystalline Orders of Electrons

André Haug1,*, Ravi Kumar1,*, Tomer Firon1, Misha Yutushui1, Kenji Watanabe2, Takashi Taniguchi3, David F. Mross1, and Yuval Ronen1,†

  • *These authors contributed equally to this work.
  • †Contact author: yuval.ronen@weizmann.ac.il
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Phys. Rev. X 16, 011039 – Published 26 February, 2026

DOI: https://doi.org/10.1103/sh8l-v7yf

Abstract

Topological and crystalline orders of electrons both benefit from enhanced Coulomb interactions in partially filled Landau levels. In bilayer graphene (BLG), the competition between fractional quantum Hall liquids and electronic crystals can be tuned electrostatically. Applying a displacement field leads to Landau-level crossings, where the interaction potential is strongly modified due to changes in the orbital wave functions. Here, we leverage this control to investigate phase transitions between topological and crystalline orders at constant filling factors in the lowest Landau level of BLG. Using transport measurements in high-quality hBN-encapsulated devices, we study transitions as a function of displacement field near crossings of N=0 and N=1 orbitals. The enhanced Landau-level mixing near the crossing stabilizes electronic crystals at all fractional fillings, including a resistive state at ν=13 and a reentrant integer quantum Hall state at ν=73. On the N=0 side, the activation energies of the crystal and fractional quantum Hall liquid vanish smoothly and symmetrically at the transition, while the N=1 transitions out of the crystal appear discontinuous. Additionally, we observe quantized plateaus forming near the crystal transition at half filling of the N=0 levels, suggesting a paired composite fermion state stabilized by Landau level mixing.

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Like ordinary matter that forms solids or liquids, electrons can also organize into distinct collective phases. When electrons are confined to two dimensions and exposed to strong magnetic fields at very low temperatures, their kinetic energy is suppressed, and interelectronic Coulomb interactions become dominant. Under these conditions, electrons typically choose between two competing phases: a topological quantum Hall liquid that flows without dissipation, or a Wigner crystal, an ordered electron lattice that minimizes mutual Coulomb repulsion. Both these phases compete for dominance, but understanding what tips the scale has been a long-standing challenge. In this work, the authors address this issue using high-quality bilayer graphene devices, in which applying a perpendicular electric field across the two layers forces the electron energy levels (Landau levels, LLs) of different orbital structures to cross. The crossing results in interorbital interactions that reshape the electron orbital wave functions, stabilizing electron crystal phases over a wide range of fractional fillings of LLs, as well as driving phase transitions between liquid and crystalline phases at specific fractional fillings (filling denotes the number of occupied LLs). Near these crossings, the authors also observed a paired electronic behavior of new topological states when LLs are half-filled, which may host exotic non-Abelian excitations relevant for quantum technologies. The experiment establishes that mixing Landau levels of different orbital structures in bilayer graphene is a powerful tunable knob to study strongly interacting electronic phases and their competitions.

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Phys. Rev. X 16, 011039– Published 26 February, 2026
  • Received 28 August 2025
  • Revised 1 December 2025
  • Accepted 26 January 2026
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