Landau level of fragile topology

Abstract

The flat bands in twisted bilayer graphene (TBG) are known to carry a new type of topology called fragile topology. Here, the authors show that the flat bands in TBG have their Hofstadter butterfly generically connected with the Hofstadter butterfly of the higher bands, which is a topological signature of the fragile topology. This leads to Landau level gaps extending over multiple bands and closing the zero magnetic field band gaps, which is detectable by transport experiments in magnetic fields.

Topics & Concepts