Quantum metric induced phases in Moiré materials

Abstract

We show that, quite generally, quantum geometry plays a major role in determining the low-energy physics in strongly correlated lattice models at fractional band fillings. We identify limits in which the Fubini-Study metric dictates the ground states and show that this is highly relevant for Moiré materials leading to symmetry breaking and interaction driven Fermi liquids. This phenomenology stems from a remarkable interplay between the quantum geometry and interaction which is absent in continuum Landau levels but generically present in lattice models where these terms tend to destabilize, e.g., fractional Chern insulators. We explain this as a consequence of the fundamental asymmetry between electrons and holes for band projected normal ordered interactions, as well as from the perspective of a self-consistent Hartree-Fock calculation. These basic insights about the role of the quantum metric, when dominant, turn an extremely strongly coupled problem into an effectively weakly coupled one, and may also serve as a guiding principle for designing material setups. We argue that this is a key ingredient for understanding symmetry-breaking phenomena recently observed in Moiré materials.