Intertwined quantum states in moiré materials

The Nature Communications study, authored by postdoctoral researchers Raul Perea Causin and Hui Liu together with Professor Emil Bergholtz, predicts the formation of so-called Hall crystals in moiré superlattices—artificial materials created by stacking atomically thin layers of semiconductors or graphene at small twist angles. These crystals are remarkable because they combine two seemingly opposite behaviors: electrons arrange themselves into an ordered crystalline structure, while maintaining topological properties associated with quantized Hall conductance. Such intertwined order challenges the traditional view that localization and topology are mutually exclusive. By showing how strong electron–electron interactions in moiré materials stabilize these hybrid states, the work offers a new conceptual framework for understanding correlated quantum phases.

Even more striking are the predictions in the Physical Review Letters paper, authored by Hui Liu and Emil Bergholtz, together with Zhao Liu (a former group member, now Professor at Zhejiang University, China). This study identifies a family of non-Abelian states of matter—phases in which the collective behavior of electrons gives rise to excitations that braid around each other in a fundamentally quantum way. These non-Abelian states are of deep theoretical interest: they realize mathematical structures long studied in physics and, could one day serve as the building blocks of fault-tolerant quantum computation.

What makes the discovery particularly surprising is that these non-Abelian states emerge in a setting where ferromagnetism, charge order, and topology closely compete with one another. The study demonstrates that strong Coulomb interactions can drive a simple metallic system into a Chern insulating state with an unexpectedly rich internal structure. In other words, rather than suppressing topology, interactions here create an entirely new topological phase with intertwined magnetic, charge, and braiding properties.

While aspects of these predictions are highly abstract, they offer new directions for fundamental research. At the same time, moiré materials are an exceptionally versatile experimental platform, and several of the proposed phenomena may be within reach of near-future experiments.
Together, these two works underscore the power of theoretical physics to chart uncharted terrain in quantum matter, revealing exotic states that could transform both fundamental understanding and technological applications of quantum materials. 

These results extend recent important work by the group on parafermions (published in Nature Communications) and build on an early theoretical prediction by Ahmed Abouelkomsan (then PhD student, now postdoc at MIT), Zhao Liu, and Emil Bergholtz (published in Physical Review Letters as an Editors’ Suggestion), which pioneered the field by showing for the first time that fractional Chern insulators can form in moiré materials—a prediction that has since been confirmed experimentally.

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Professor Emil Bergholtz

Postdoc Raul Perea Causin

Postdoc Hui Liu