Moiré patterns are well known in the visual arts and textile industries—the term comes from the textured patterns seen in mohair silk fabrics. It arises whenever two periodic structures are superimposed, giving rise to new periodicities. Remarkably, applying these ideas to atomically thin materials, the coupling between the layers enables designer materials where properties like bandwidth, electron velocity, and band topology can be controllably altered. With more than 1,000 possible “easily exfoliatable” materials to play with, this opens the possibility of billions of designer band structures with applications to both fundamental science and technology.

In this talk, I will focus on two recent developments. First, I will show that when the relative rotation between two sheets becomes small, lattice relaxation and electrostatic interactions are not small corrections but decisive ingredients that reshape the electronic structure of moiré materials [1,2].  For twisted bilayer graphene, these effects create a “magic window” of twist angles which stabilize a Lifshitz transition to an ultraflat, heavy-fermion–like Fermi surface pinned to the Fermi energy. Second, I will discuss superconductivity and electron hydrodynamics—two directions that push beyond conventional paradigms. Superconductivity in twisted bilayer graphene may arise from purely electronic collective modes, while new evidence shows its extreme sensitivity to Coulomb screening, consistent with unconventional pairing [3].  I will also discuss the hydrodynamic regime in which electrons flow like a viscous liquid. Our combined theory–experiment program shows that in this regime the conductivity is given by the sum of universal and dissipative Drude-like terms, validated by measurements of ambipolar hydrodynamic transport [4].  Both these directions emphasize that moiré materials are not only playgrounds for strong correlations, but also testing grounds for broader concepts in quantum matter.

References
[1] M.M. Al Ezzi, G.N. Pallewela, C. De Beule, E.J. Mele, and S. Adam, Analytical Model for Atomic Relaxation in Twisted Moiré Materials, Phys. Rev. Lett. 133, 266201 (2024).

[2] D. R. Klein, U. Zondiner, A. Keren, J. Birkbeck, A. Inbar, J. Xiao, M. Sidorova, M. M. Al Ezzi, L. Peng, K. Watanabe, T. Taniguchi, S. Adam, and S. Ilani,  “Imaging the Sub-Moiré Potential Landscape using an Atomic Single Electron Transistor”, arXiv:2410.22277 (2024).

[3] J. Barrier, L. Peng, S. Xu, V.I. Fal’ko, K. Watanabe, T. Taniguchi, A.K. Geim, S. Adam, and A.I. Berdyugin, Coulomb screening of superconductivity in magic-angle twisted bilayer graphene, arXiv:2412.01577 (2024).

[4] C. Tan, D.Y.H. Ho, L. Wang, J.I.A. Li, I. Yudhistira, D.A. Rhodes, T. Taniguchi, K. Watanabe, K. Shepard, P.L. McEuen, C.R. Dean, S. Adam, and J. Hone, Dissipation-enabled hydrodynamic conductivity in a tunable bandgap semiconductor, Sci. Adv. 8, eabi8481 (2022).