Topological mini-bands and electron-phonon interaction in Moiré materials

A new class of quantum materials, Moiré superlattices, is rapidly emerging as a powerful and flexible platform to explore correlated physics, superconductivity, and topological physics. In the first part of this talk, I will discuss how to engineer topological minibands using Moiré superlattices. I will focus on the possibility of realizing isolated topologically non-trivial Moiré minibands in a topological insulator film under a Moiré superlattice. I will show that Coulomb interaction can drive this system into the quantum anomalous Hall state when the non-trivial Moiré miniband is half filled. In the second part of the talk, I will describe the recent experimental observation of replicas of the flat bands in superconducting magic-angle twisted bilayer graphene unaligned with its hexagonal boron nitride substrate. Motivated by this experimental observation, we developed an analytic theory to describe the interaction between electrons and K-phonons to study its influence on superconductivity in the bare bands of twisted bilayer graphene.

[1] Z2-Nontrivial Moiré Minibands and Interaction-Driven Quantum Anomalous Hall Insulators in Topological Insulator Based Moiré Heterostructures, Kaijie Yang, Zian Xu, Yanjie Feng, Frank Schindler, Yuanfeng Xu, Zhen Bi, B. Andrei Bernevig, Peizhe Tang, Chao-Xing Liu, arXiv:2304.09907, 2023.

[2] Electron-K-Phonon Interaction in Twisted Bilayer Graphene, Chao-Xing Liu, Yulin Chen, Ali Yazdani, B. Andrei Bernevig, arXiv:2303.15551, 2023.

[3] Strong Inter-valley Electron-Phonon Coupling in Magic-Angle Twisted Bilayer Graphene, Cheng Chen, Kevin P. Nuckolls, Shuhan Ding, Wangqian Miao, Dillon Wong, Myungchul Oh, Ryan L. Lee, Shanmei He, Cheng Peng, Ding Pei, Yiwei Li, Shihao Zhang, Jianpeng Liu, Zhongkai Liu, Chris Jozwiak, Aaron Bostwick, Eli Rotenberg, Chu Li, Xu Han, Ding Pan, Xi Dai, Chaoxing Liu, B. Andrei Bernevig, Yao Wang, Ali Yazdani, Yulin Chen, arXiv:2303.14903, 2023.

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