Dispersionless electrons, emergent phases, and quantum geometry

IQOQI Quantum Seminar

dvancements in new-generation quantum materials have unveiled a plethora of emergent phases, from unconventional superconductors to Fractional Chern Insulators. Beyond their unique bandstructures, such materials, represented by twisted transition metal dichalcogenides and twisted multilayer graphene, exhibit nearly dispersionless quantum states ("flat bands") with distinctive quantum geometrical properties. A new paradigm, centered on the quantum geometry of flat bands, is gaining momentum in understanding the nature of these phases. Quantum geometry, which quantifies the proximity between adjacent quantum states in Hilbert space, has been instrumental in quantum information science, but had been largely overlooked in solid-state experiments. In this seminar, we will explore the quantum transport formalism through the lens of quantum geometry and demonstrate the construction of novel observables. As a practical application, we propose an innovative experimental approach to measure the ultra-narrow topological band gap using quantum noise measurements. Time permitting, we discuss importance of quantum geometry for developing new-generation Fractional Chern insulators, and the challenge of constructing Fractional Chern insulators supporting non-abelian anyons.

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