Correlated Chern insulators and nonlinear transport in magic-angle twisted bilayer graphene

Yen-Ting Liu^1*, Kuo-En Chang¹, Yu-Chiang Hsieh¹, Ying-Mei Yang², Kenji Watanabe³, Takashi Taniguchi⁴, Tse-Ming Chen^1,2

¹Department of Physics, National Cheng Kung University, Tainan, Taiwan
²Center for Quantum Frontiers of Research & Technology (QFort), National Cheng Kung University, Tainan, Taiwan
³Research Center for Electronic and Optical Materials, National Institute for Materials Science, Institute for Materials Science, Tsukuba, Japan
⁴Research Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan

* Presenter:Yen-Ting Liu, email:l26134039@gs.ncku.edu.tw

The quantum geometry of band structures comprises two components: the quantum metric (real part) and the Berry curvature (imaginary part), both crucial in governing electron behavior in momentum space. In magic-angle twisted bilayer graphene (MATBG), nonzero Berry curvature emerges in the strongly interacting regime, giving rise to topologically nontrivial Chern bands. Distinct from conventional topological matter that obeys a single-particle framework, the MATBG Chern insulator exemplifies a correlation-induced topological phase in which electron-electron interactions reconstruct the flat-band and its associated quantum geometry. However, most studies have focused on the topological aspects and relied on linear anomalous Hall effects, while how the underlying geometrical properties, particularly the Berry curvature, evolve under strong electron-electron interactions remains elusive.
Here, we fabricated high-quality MATBG devices and observed strongly correlated Chern insulating state accompanied by anomalous Hall effect at the band filling factor of ν = 3. Through second-harmonic transport measurements in this correlated regime, we report the observation of nonlinear anomalous Hall effect in MATBG, which we attribute to the emergence of Berry curvature dipoles. Our findings reveal interaction-driven nonlinear quantum transport in MATBG and may open new avenues for understanding the interplay between quantum geometry and strong correlation effects.

Keywords: magic-angle twisted bilayer graphene, Chern insulator, strongly correlated systems, nonlinear anomalous Hall effect, Berry curvature