Hofstadter butterflies for flat bands

TL;DR

This paper explores the Hofstadter butterfly spectrum for models with flat bands, revealing how magnetic fields affect their topological and interference-based origins, with implications for anomalous orbital magnetism.

Contribution

It introduces analysis of Hofstadter spectra for flat bands, distinguishing topological from interference origins and their magnetic responses.

Findings

Magnetic fields preserve topologically derived flat bands.

Dispersions emerge anomalously in interference-based flat bands.

Implications for understanding orbital magnetism in flat band systems.

Abstract

Hofstadter's diagram, or the energy spectrum against the magnetic field in tight-binding systems, is obtained for the models having flat (dispersionless) one-electron band(s) that have originally been proposed for itinerant spin ferromagnetism. Magnetic fields preserve those flat bands that arise from a topological reason, while dispersions emerge in a singular manner for the flat bands arising from interference, implying an anomalous orbital magnetism.