Geometric characterization of anomalous Landau levels of isolated flat bands

TL;DR

This paper reveals that isolated flat bands can exhibit anomalous Landau level spreading outside zero-field bounds, governed by wave-function geometry, challenging traditional semiclassical expectations.

Contribution

It introduces a new class of flat band systems with anomalous Landau level spreading governed by cross-gap Berry connection, highlighting the role of wave-function geometry.

Findings

Anomalous Landau level spreading occurs outside zero-field bounds in certain flat bands.

Wave-function geometry, via Berry connection, governs the Landau level behavior.

Symmetry constraints significantly influence Landau level spreading in 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.