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Main Authors: Kolář, Kryštof, Yang, Kang, von Oppen, Felix, Mora, Christophe
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2507.00130
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author Kolář, Kryštof
Yang, Kang
von Oppen, Felix
Mora, Christophe
author_facet Kolář, Kryštof
Yang, Kang
von Oppen, Felix
Mora, Christophe
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2507_00130
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Robustness of real-space topology in moiré systems
Kolář, Kryštof
Yang, Kang
von Oppen, Felix
Mora, Christophe
Mesoscale and Nanoscale Physics
Strongly Correlated Electrons
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.
title Robustness of real-space topology in moiré systems
topic Mesoscale and Nanoscale Physics
Strongly Correlated Electrons
url https://arxiv.org/abs/2507.00130