11/16/2021 Quantum Matter in Mathematics and Physics

Title: Quantum Geometric Aspects of Chiral Twisted Graphene Models

Abstract: “Moire” materials produced by stacking monolayers with small relative twist angles are of intense current interest for the range of correlated electron phenomena they exhibit. The quench of the kinetic energy means that the interacting physics is controlled by the interplay between the interaction scale and intrinsic quantum geometries of the flat band states, in particular the Berry curvature and the Fubini-Study metric, which are in general spatially non-uniform. We show that the analytical solution of the twisted bilayer graphene wavefunction in the chiral limit has a special band geometry, endowing the Brillouin zone with a complex structure. This talk focus on the origin of the momentum space complex structure, concrete models that realize it, and its implications to electron-electron interactions. We first show the momentum space complex structure in Chern number C=1 flatbands implies the Bloch wavefunction to exhibit an exact correspondence to the lowest Landau level in the dual momentum space [2]. We present a generalization of the Haldane pseudopotential concept to deal with interacting problems in these bands and discuss experimental implications [2]. We also present an analytically solvable multi-layer generalized chiral graphene model, which exhibits arbitrarily high Chern number and ideal quantum geometries [3]. Numerical studies of interacting particles indicate model fractional Chern insulators without Landau level analogues, characterized by exact degeneracies and infinite particle entanglement spectra gaps [3]. References:

[1] Jie Wang, Yunqin Zheng, Andrew J. Millis, Jennifer Cano (Phys. Rev. Research 3, 023155)
[2] Jie Wang, Jennifer Cano, Andrew J. Millis, Zhao Liu, Bo Yang (arXiv: 2105.07491, to appear in PRL)
[3] Jie Wang, Zhao Liu (arXiv: 2109.10325)

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