Kerr and Faraday rotations in topological flat and dispersive band structures

Abstract

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

arXiv comment10 pages, 4 figures

References in corpus (26)

• Berry Phase Effects on Electronic Properties
• Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene
• Intrinsic quantized anomalous Hall effect in a moiré heterostructure
• High temperature fractional quantum Hall states
• Fractional quantum Hall states at zero magnetic field
• Nearly-flat bands with nontrivial topology
• A new electromagnetic mode in graphene
• Fractional quantum Hall effect in the absence of Landau levels
• Giant Magneto-optical Kerr Effect and Universal Faraday Effect in Thin-film Topological Insulators
• Topological Flat Band Models and Fractional Chern Insulators
• Topological flat band models with arbitrary Chern numbers
• Tuning Chern Number in Quantum Anomalous Hall Insulators
• Magneto-Optical Faraday and Kerr Effects in Topological Insulator Films and in Other Layered Quantized Hall Systems
• Visualization of the flat electronic band in twisted bilayer graphene near the magic angle twist
• Optical Hall conductivity in ordinary and graphene QHE systems
• Fractional Chern Insulators in Harper-Hofstadter Bands with Higher Chern Number
• Polar Kerr Effect and Time Reversal Symmetry Breaking in Bilayer Graphene
• Anomalous Hall effect, magneto-optical properties, and nonlinear optical properties of twisted graphene systems
• Origin of the flat band in heavily Cs doped graphene
• Optical properties of magnetically doped ultra-thin topological insulator slabs
• Transfer matrix approach for the Kerr and Faraday rotation in layered nanostructures
• Valley symmetry breaking and gap tuning in graphene by spin doping
• Determination of intrinsic lifetime of edge magnetoplasmons
• Nonlinear Optical Response of Spin Density Wave Insulators
• Kerr effect in tilted nodal loop semimetals
• Intra-cell dynamics and cyclotron motion without magnetic field