Kerr and Faraday rotations in topological flat and dispersive band structures

Abstract Integer quantum Hall (IQH) states and anomalous (QAH) show the same static dc response but distinct dynamical ac response. In particular, conductivity profile σ yx ( ω ) is sensitive to band shape of QAH states. For example, dispersive bands shows resonance without a sign change at gap while IQH cyclotron energy. We argue by flattening bands, should recover that flat Landau in IQH, thus it necessary know origin change. Taking topological lattice model with tunable bandwidth, we found not van Hove singularity energy bands. limit small recovers Because response, these exhibit giant polarization rotation ellipticity reflected waves (Kerr effect) order fine structure constant transmitted (Faraday resembles ). Our results serve as simple guide optical characterization for