**Time/Venue **Wednesday, April 13 at 2:00 pm Pacific Time in Physics South 402 and via Zoom:

https://berkeley.zoom.us/j/99523499113pwd=REovb3pyam03WXQwbEhrU3dqNHZvdz09

Meeting ID: 995 2349 9113 Passcode: 600704**Host** Joel Moore / Ehud Altman**Title** Quantum Geometry and Its Application to Fractional Chern Insulators in Twisted Bilayer Graphene**Abstract** In contrast to the fractional quantum Hall (FQH) effect, where electron density fixes the applied magnetic field, fractional Chern insulators (FCIs) can realize FQH states in comparatively weak or even zero magnetic fields. Previous theoretical work highlighted magic angle graphene (TBG) as a promising FCI platform, satisfying the twin requirements of flat bands and lowest-Landau-level-like quantum geometry. Indeed, recent experiments have demonstrated FCIs in magic angle graphene with weak magnetic fields.

In the first part of this talk I will discuss how the humble position operator naturally leads to ideal (holomorphic) quantum geometry and present the generalization to many bands and higher Chern numbers.

In the second part of the talk, I will apply combine ideal geometry with numerics and the Hofstadter butterfly to answer three practical questions about the FCIs observed in TBG:1. Why do FCIs appear in TBG?2. Why have they only appeared at finite magnetic field so far?3. What are the experimental parameters required for FCIs at zero magnetic field?

This talk is based on arXiv: 2107.10854, arXiv: 2112.13837, and forthcoming work.

# Emergent Phenomena 290S/QM Speaker Daniel Parker (Harvard) Wednesday, April 13 at 2:00 pm

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