Research Projects

Quantum materials whose properties can be altered by external means have garnered tremendous attention in the last decades. Of prominence are two-dimensional layered structures, also known as emergent materials, which exhibit remarkable collective phenomena when subjected to periodic mechanical strain or twists between the layers. A key element driving the intense research on twisted heterostructures is the potential for band structure engineering and the notable capacity to produce flat bands that are characterized by zero dispersion (in other words, the kinetic energy of the electrons in flat bands is quenched). Because of the negligible kinetic energy of electrons occupying such bands, they exhibit dramatic behavior in response to interactions. Electrons in gapless flat bands show markedly distinct responses both in noninteracting and interacting scenarios. Even the simplest setting is rich: band degeneracies involving one gapless flat band and a quadratically dispersive band can be classified into singular and non-singular categories based on the underlying quantum geometry and the singularity of the Bloch wavefunction at the degeneracy point. For systems with multiple flat bands, the degeneracy point represents a higher-spin generalization of the S = 1/2 Dirac cones, and a topological classification can be established in terms of the degeneracy of the flat bands and the homotopy classes of the (Bloch) Hamiltonian manifolds around the degeneracy points. Among them, the triple degeneracy is particularly intriguing as it encompasses the recently discovered low-energy nexus fermions found in certain topological symmorphic crystalline metals with unusual magnetic transport properties. Despite the significant theoretical and experimental advancements, a comprehensive characterization of the response of fermions in singular flat bands and nexus points to uniform and periodic gauge fields remains lacking. Identifying this knowledge gap and based on our preliminary investigation, the motivation for this work is compelling: we seek to address the following fundamental questions: given the inevitable electronic correlations in quantum materials, what novel collective phenomena and intertwined orders arise from the interplay of interactions and periodic fields? What new quantum information can we extract from the entanglement structure of the ground states of these fermions? In this pursuit, the proposed research aims to illuminate robust and exotic responses of the aforementioned topological band structures to periodic gauge fields, providing explanations for several interesting recent findings in heterostructures, topological metals, and semimetals. By extending into the interacting scenario, we further seek to discover novel states of correlated topological quantum matter that are simulatable on modern quantum processors, which could have a significant impact on the field of quantum computations and quantum information processing.