Geometric characterization of anomalous Landau levels of isolated flat bands

Abstract

According to the Onsager's semiclassical quantization rule, the Landau levels of a band are bounded by its upper and lower band edges at zero magnetic field. However, there are two notable systems where the Landau level spectra violate this expectation, including topological bands and flat bands with singular band crossings, whose wave functions possess some singularities. Here, we introduce a distinct class of flat band systems where anomalous Landau level spreading (LLS) appears outside the zero-field energy bounds, although the relevant wave function is nonsingular. The anomalous LLS of isolated flat bands are governed by the cross-gap Berry connection that measures the wave-function geometry of multi bands. We also find that symmetry puts strong constraints on the LLS of flat bands. Our work demonstrates that an isolated flat band is an ideal system for studying the fundamental role of wave-function geometry in describing magnetic responses of solids.

10+8 pages, 5+3 figures

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Cited by in corpus (8)

• General construction of flat bands with and without band crossings based on wave function singularity
• Hofstadter Topology with Real Space Invariants and Reentrant Projective Symmetries
• Fractal-like photonic lattices and localized states arising from singular and nonsingular flatbands
• Berry Phase and Topology in Ultrastrongly Coupled Quantum Light-Matter Systems
• Flat bands with band crossings enforced by symmetry representation
• Landau Levels of the Euler Class Topology
• Fragile topological phase on the triangular kagome lattice and its bulk-boundary correspondence
• Unconventional gapless semiconductor in an extended martini lattice in covalent honeycomb materials