Quantum Simulation and Many-Body Physics in Moiré Bilayers*

Moiré superlattices form in van der Waals bilayers with a small lattice mismatch or misalignment. The moiré pattern produces spatial modulation and can dramatically alter electronic properties. I will present theoretical proposals of using moiré bilayers as a quantum simulation platform to realize model Hamiltonians, and discuss many-body effects that are magnified when the moiré bands are nearly flat. In semiconducting transition metal dichalcogenide (TMD) heterobilayers, isolated flat moiré bands can be used to simulate Fermi-Hubbard model on a triangular lattice [1], in which parameters such as bandwidth, interaction strength, and band filling are widely tunable. When the two layers are formed from the same TMD, holes in ±K valleys move in a layer-pseudospin skyrmion texture in real space. The low-energy moiré bands then realize Kane-Mele model [2], providing a platform to study interplay between topology and correlation. Excitons in twisted TMD bilayers also experience moiré potential, which can be used to design topological exciton bands and to simulate Bose-Hubbard model [3]. Twisted bilayer graphene (TBLG) is a distinct example where the effective lattice theory does not simply map to any known model Hamiltonian. Motivated by the observed superconductivity, I will present a candidate theory of phonon-mediated superconductivity in TBLG [4]. Phonon fluctuations lead to both s-wave and d-wave pairings. New phenomena of the d-wave superconductivity in moiré pattern will be discussed.

[1] F. Wu, T. Lovorn, E. Tutuc, A. H. MacDonald, Phys. Rev. Lett. 121, 026402 (2018).
[2] F. Wu, T. Lovorn, E. Tutuc, I. Martin, A. H. MacDonald, arXiv:1807.03311.
[3] F. Wu, T. Lovorn, A. H. MacDonald, Phys. Rev. Lett. 118, 147401 (2017).
[4] F. Wu, A. H. MacDonald, I. Martin, arXiv:1805.08735.