2025/06/30 by Kryštof Kolář, Kolář, Kryštof, Kang Yang +5
Materials Science · Physics and Astronomy · #Chemical and Physical Properties of Materials #FOS: Physical sciences #Graphene research and applications #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Strongly Correlated Electrons (cond-mat.str-el) #Topological Materials and Phenomena
paper · pdf · doi:10.48550/arxiv.2507.00130
openalex publication_date 2025/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The appearance of fractional Chern insulators in moiré systems can be rationalized by the presence of a fictitious magnetic field associated with the spatial texture of layer-resolved electronic wavefunctions. Here, we present a systematic study of real-space topology and the associated fictitious magnetic fields in moiré systems. We first show that at the level of individual Bloch wavefunctions, the real-space Chern number, akin to a Pontryagin index, is a fragile marker. It generically vanishes except for specific limits where the Bloch functions exhibit fine-tuned zeroes within the unit cell, such as the chiral limit of twisted bilayer graphene (TBG) or the adiabatic regime of twisted homobilayer transition metal dichalcogenides (TMD). We then show that these limitations do not apply to textures associated with ensembles of Bloch wavefunctions, such as entire bands or the ensemble of states at a given energy. The Chern number of these textures defines a robust topological index protected by a spectral gap. We find that symmetries constrain it to be nonzero for both twisted TMDs and TBG across all twist angles and levels of corrugation, implying experimental signatures in scanning tunneling microscopy measurements. We also study real-space topology within the topological heavy fermion model of TBG, finding that the real-space topological features are supported only by the light c-electrons.