Exactly closed density algebra in ideal flatbands and implications (Jul. 3, 2023)

  • Published: 2023-06-27

Time: 10:30am, July 3 (Monday), 2023

Location: Room 401, No. 7 Building, Kavli ITS, UCAS


Speaker: Jie Wang 王捷 (Harvard University)



Fractional Chern insulators (FCI) are the zero-field analogy of fractional quantum Hall (FQH) effect. How to stabilize FCI in interacting topological flatbands is important to both theory and experiment. It is commonly believed FCI is less stable than FQH, due to the inhomogeneous quantum geometries of Bloch states and consequently the absence of closed density algebra (Girvin-MacDonald-Platzmann algebra). In this talk, I will challenge such common lore by presenting a large family of flat band systems dubbed ideal flatbands [1-3], which exhibit a couple of universal and exact properties (exact density algebra, universal wavefunction form) coexisting with inhomogeneous quantum geometries. Consequently, FCIs are provable to be exact ground states in ideal flatbands when interaction is short ranged, regardless of the inhomogeneity of quantum geometries. Ideal flatbands also provides a simple single-particle criteria for the stability of FCI in realistic materials. Recently theoretical and experimental work shows moiré system as promising platform for realizing FCI. In the end of the talk, I will talk about the application of ideal band theory to twisted materials (twisted MoTe2) [4] where optical signature of zero-field FCI was recently reported.


[1] Exact Landau level description of geometry and interaction in a flatband. JW, Cano, Millis, Liu, Yang (PRL 127, 246403)

[2] Hierarchy of ideal flatbands in chiral twisted multilayer graphene models. JW and Z. Liu (PRL 128, 176403)

[3] Origin of model fractional Chern insulators in all topological ideal flatbands. JW, S. Klevtsov and Z. Liu (PRR 5, 023167)

[4] Composite Fermi liquid at zero magnetic field in twisted MoTe2. Dong, JW, Ledwith, Vishwanath, Parker (arXiv: 2306.01719).