Theory of Topological and Competing Orders in Quantum Materials

Principal Investigator: Luiz H. Santos, Emory University, Atlanta, Georgia

This project aims to uncover the principles governing the formation of topological phases of matter and the dominant interaction mechanisms that give rise to these phases and their competing orders. Such phases exhibit topological degeneracies and fractional excitations—phenomena of deep fundamental interest with potential impact on quantum information platforms and low-dissipation electronic systems. Realizing them in physical systems remains a major challenge at the interface of quantum materials and quantum information science.

This research explores a new frontier of topological and competing electronic orders in van der Waals quantum materials. These systems offer exceptional tunability through layer composition, twist angle, and external fields, but their intricate band structures pose significant challenges for modeling correlated quantum phenomena. This project aims to optimize the interplay between electronic band structure and interactions in Moiré materials, a key ingredient for stabilizing topological orders. It develops a theoretical framework for fractionalized phases with Abelian statistics by characterizing new classes of composite fermions. They emerge in systems with strong lattice effects, where electronic bands are characterized by non-uniform Berry curvature and nontrivial quantum geometry. These investigations will shed light on the organizing principles of fractional matter and coexisting or competing phases across transition metal dichalcogenide and graphene heterostructures and may uncover unanticipated pathways for their realization.

The project will also explore new mechanisms for realizing non-Abelian topological matter in Moiré platforms. The focus is on composite fermion pairing and interfaces between superconductors and fractional Abelian matter. By examining the role of quantum geometry, pairing instabilities, and engineered interfaces, the research aims to identify candidate routes toward non-Abelian phases without external magnetic fields. This scientific activity aligns with key priorities of the DOE-BES Theoretical Condensed Matter Physics program, including electron correlations, topological states of matter, and unconventional superconductivity.