Speaker
Description
Two-dimensional moiré superlattices have emerged as ideal systems to study the many-body interactions and correlated states in topologically nontrivial energy bands. The filling factor of the moiré energy band can be changed by varying the gate voltage, while other electronic properties can be modified by easily accessible external factors such as an external electric or magnetic fields, strain or a twist angle between the atomic layers forming a moiré pattern. Fractional Chern insulators are the zero magnetic field analog of the fractional quantum Hall (FQH) effect. They appear in fractionally filled Chern bands and were recently observed in twisted MoTe2 and in rhom-bohedral graphene aligned with hexagonal boron nitride. These fractionalized states in moiré systems are expected to be in the same universality class as their counterparts in Landau levels, but the periodic potential and quantum geometry can have significant effects on physical observables. In this work, we analyze stability and optical properties of fractional Chern insulators when their quantum geometric properties differ from standard fractional quantum Hall (FQH) states in a Landau level. This can be quantified by calculation of deviation from a uniform Berry curvature or Girvin-MacDonald-Platzman (GMP) algebra. We determine ideal quantum geometry conditions where Landau-level-like correlations at long length scales are expected. Moving away from this ideal point by varying model parameters, we investigate the effect of quantum geometry on collective excitations of FCI’s and their coupling to light.
