#  Colloquium by Prof. Eslam Khalaf: "From quantum Hall to Hubbard physics in twisted bilayer graphene: a unified framework for strongly correlated topological bands" 

 



####  calendar\_today Date and Time 

 **April 1, 2024** 

 04:30PM - 05:30PM EDT 

####  pin\_drop Location 

 **Jefferson 250**  



 

 



 

 Understanding the behavior of strongly correlated materials is one of the central goals of condensed matter physics. A major recent milestone towards this goal was the creation of a new class of artificially engineered materials where correlations can be controllably tuned. These materials, referred to as moiré materials, are built by stacking two-dimensional atomically thin sheets to create long wavelength periodic patterns. In this talk, I will discuss the most prominent member of this family, twisted bilayer graphene (TBG), consisting of two graphene sheets that are twisted at a relative angle. Understanding correlations in TBG requires an understanding not only of the topological character of the electronic wavefunction but also of their geometric and analytic features. I will show how we can combine basic facts about the geometry, topology, and symmetry of the wavefunctions, to formulate a comprehensive understanding of the rich phase diagram of TBG which elegantly unifies seemingly incompatible features such as band topology and fluctuating moment physics. I will also show how this formulation can be used to describe different phases such as correlated insulators, superconductors and quantum anomalous Hall phases. This description not only enables experimental predictions but also offers an intuitive understanding of the nature of correlated phases by relating them to two of the more well-studied paradigms of strong correlations: the Hubbard model and the quantum Hall problem. At the end, I will discuss future possibilities enabled by tunable heterostructures including the study of topology and correlations in artificial quasicrystals.

 **Bio**: Eslam Khalaf got his PhD in 2017 from the Max Planck institute working on problems of topology and localization for which he was awarded the Otto Hahn medal by the Max Planck Society. Between 2018 and 2022, he was a postdoctoral fellow at Harvard working on problems of topology and correlations, particularly in the context of moiré systems. In fall 2022, he started an assistant professor position at the University of Texas at Austin. In fall 2023, he moved back to Harvard for an assistant professor position.



 

 

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