Shaffique Adam
Washington University, St. Louis
Designer Flat Bands and Emergent Quantum Properties of Moiré Systems
Location: 1080 Physics Research Building
Faculty Hosts: Jeanie Lau, Marc Bockrath
Abstract: 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, this opens the possibility of billions of designer band structures with applications to both fundamental science and technology.
I will begin with lattice relaxation, which reorganizes local stacking into twist-dependent displacement fields. At large twist angles, we develop analytical scaling theory that yields divergence-free shear patterns that agree quantitatively with molecular dynamics and DFT benchmarks [1]. At small twist angles, the system enters a strong-coupling regime where unfavorable stackings collapse, forming a soliton network. We develop an analytical theory for this regime and benchmark against state-of-the art numerical calculations [2].
Next, I will discuss Hartree and exchange interactions [3], which are comparable in magnitude to the moiré bandwidth. The Hartree potential tracks the relaxed stacking pattern and produces large electrostatic shifts even at charge neutrality. Exchange interactions further redistribute Berry curvature and reorder the minibands.
Finally, I will show how relaxation and interactions combine to produce a magic angle window rather than a single fine-tuned value. Within this window, the bandwidth collapses, the Fermi surface undergoes a Lifshitz transition, and the system develops an ultraflat, heavy-fermion–like band pinned to the Fermi energy [4]. These results highlight how moiré materials magnify atomic-scale physics into emergent quantum phenomena, offering a versatile platform for exploring strongly correlated electron systems.
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] C. De Beule, G.N. Pallewela, M.M. Al Ezzi, L. Peng, E. J. Mele, and S. Adam, Theory for Lattice Relaxation in Marginal Twist Moirés, arXiv:2503.19162 (2025).
[3] L. Peng, G. Vignale, and S. Adam, Many-body perturbation theory for moiré systems, Phys. Rev. B 112, 075146 (2025), Editor’s Suggestion.