Geometric Aspects of Quantum Matter

'Topology' and 'geometry' are an important math concepts that have influenced the modern condensed matter physics. 'Topology' determines the global aspects of quantum matters such as classification, Hall conductivity, robust edge states etc. In contrast, 'geometry' is local and determines the details of electrons' coherence, the stability, and how they response to external probes.

I am particularly interested in how the quantum geometries of the Bloch wavefunction influence the stabilities of interacting phase, and contribute to the development of Theory of Ideal Flatbands [1,2].

My recent seminar talk on this topic titled "Quantum Geometric Aspects of Chiral Twisted Graphene Models" at CMSA Harvard is available on YouTube! Video link here.

[1] Jie Wang, Jennifer Cano, Andrew J. Millis, Zhao Liu and Bo Yang (2021). Exact Landau Level Description of Geometry and Interaction in a Flatband. PhysRevLett.127.246403

[2] Jie Wang and Zhao Liu (2021). Hierarchy of Ideal Flatbands in Chiral Twisted Multilayer Graphene Models. arXiv:2109.10325 (PRL accepted, Editor's Suggestion)

[3] Junkai Dong, Jie Wang, Liang Fu (2022). Dirac electron under periodic magnetic field: Platform for fractional Chern insulator and generalized Wigner crystal. arXiv 2208.10516.

[4] Jie Wang, Semyon Klevtsov and Zhao Liu (2021). Origin of Model Fractional Chern Insulators in All Topological Ideal Flatbands: Explicit Color-entangled Wavefunction and Exact Density Algebra. arXiv: 2210.013487 (2022).