Informal CMTC Seminar: Xiao Li

Speaker: Xiao Li (City University of Hong Kong)
Title: Correlated Topological Phases in Graphene Moiré Systems: A Theoretical Account of Chern States and Quantum Geometry
Abstract: Graphene-based moiré systems host flat bands whose nontrivial quantum geometry drives integer and fractional Chern insulators and other correlated topological phases, tunable by twist angle, stacking alignment, displacement field, and magnetic field. In this talk I will present a theoretical framework, developed in close partnership with three experiments [1-3], for how these knobs control the emergence and stability of such states—and for what the measurements actually probe. Modeling transport in rhombohedral multilayer graphene aligned with hexagonal boron nitride (RMG/hBN) [1], I show how the moiré potential and band structure separate two regimes: alignment orientation reshapes correlations in the moiré-proximal regime but is largely irrelevant to Chern insulator formation in the moiré-distant regime, where the moiré periodicity instead sets stability. This picture accounts for the observed anomalous Hall effect and the competing integer, extended, and trivial insulators near ν = 1 in one specific alignment. On the hole-doped side of rhombohedral tetralayer graphene/hBN [2], the same band-structure analysis explains a hierarchy of high-Chern-number states—C = −4 at ν = −1 and symmetry-broken C = +3, ±2, ±1 at fractional fillings ν ≈ −2.5—and their sensitivity to moiré wavelength across alignments. Finally, turning to a distinct moiré platform—twisted double bilayer graphene—I will develop orbital magnetic susceptibility as a thermodynamic probe of electronic structure. Comparing theory with scanning SQUID-on-tip imaging [3], I show that local susceptibility maps encode Lifshitz transitions, Chern transitions, and interaction-driven band reconstruction invisible to transport, and that the susceptibility gives thermodynamic access to wavefunction quantum geometry beyond Berry curvature—with the distribution of quantum geometry directly imprinted in and recoverable from the signal. Together these results frame band geometry as the organizing principle behind correlated topology in van der Waals systems.
References:
[1] C. Li, et al., arXiv:2505.01767. 
[2] C. Zheng, et al., arXiv:2604.26643. 
[3] W. Zhi, et al., in progress.