Anomalous Landau levels and quantum oscillation in rotation-invariant insulators

Abstract

Landau levels in certain models are known to protrude into the zero-field energy gap. These are known as anomalous Landau levels (ALLs). We study whether ALLs can lead to Fermi-surface like quantum oscillation in the absence of a zero-field Fermi surface. Focusing on two-dimensional multi-band low-energy models of electrons with continuous rotation symmetry, we show that an effective-band description, akin to the semiclassical treatment of Landau level problems in metals, can be used to predict the Landau level spectrum, including possible ALLs. This description then describes ALL induced quantum oscillation for certain insulating models, which we demonstrate through numerical calculations.

10 pages, 4 figures

References in corpus (25)

• The electronic properties of graphene
• Quantized Anomalous Hall Effect in Magnetic Topological Insulators
• The electronic properties of bilayer graphene
• High-precision realization of robust quantum anomalous Hall state in a hard ferromagnetic topological insulator
• Trajectory of Anomalous Hall Effect toward the Quantized State in a Ferromagnetic Topological Insulator
• Scale-Invariant Dissipationless Chiral Transport in Magnetic Topological Insulators beyond the Two-Dimensional Limit
• Colloquium: Quantum anomalous Hall effect
• Quantum Anomalous Hall Effect in Graphene Proximity Coupled to an Antiferromagnetic Insulator
• Precise quantization of anomalous Hall effect near zero magnetic field
• Topological Insulators on the Lieb and Perovskite Lattices
• Flat Chern Band in a Two-Dimensional Organometallic Framework
• A new magnetic field dependence of Landau levels on a graphene like structure
• Spin-orbit driven band inversion in bilayer graphene by van der Waals proximity effect
• Quantum Oscillations of Electrical Resistivity in an Insulator
• Anomalous Quantum Oscillations in a Heterostructure of Graphene on a Proximate Quantum Spin Liquid
• Anomalous Quantum Oscillations of Interacting Electron-hole Gases in Inverted Type-II InAs/GaSb Quantum Wells
• Tunable Intrinsic Plasmons due to Band Inversion in Topological Materials
• Quantum oscillations of magnetization in the tight-binding electrons on honeycomb lattice
• Quantum oscillations in the zeroth Landau Level and the serpentine Landau fan
• Aperiodic quantum oscillations of particle-hole asymmetric Dirac cones
• Three-quarter Dirac points, Landau levels and magnetization in $\alpha$-(BEDT-TTF)${}_2$I${}_3$
• Revisiting the magnetic responses of bilayer graphene from the perspective of the quantum distance
• Hall map and breakdown of Fermi liquid theory in the vicinity of a Mott insulator
• Unconventional quantum oscillations and evidence of nonparabolic electronic states in quasi-two-dimensional electron system at complex oxide interfaces
• The Detection of Unconventional Quantum Oscillations in Insulating 2D Materials