Beecroft Building, Department of Physics, University of Oxford, Parks Road, Oxford, OX1 3PU
Professor Valentin Crépel, University of Toronto
Abstract
Realizing the promise of moiré materials: from material selection to operating conditions and design
Van der Waals heterostructures—stacks of two‑dimensional materials held together by weak, non‑chemical interactions—have attracted immense interest because their layer‑by‑layer assembly offers unprecedented freedom in material design. The combination of constituents with distinct properties, together with the application of external fields creates a vast combinatorial landscape, fueling the vision of moiré materials as programmable quantum simulators [1].
However, this very richness renders moiré materials subject to the curse of dimensionality: identifying which material combinations, operating conditions, and geometries are best suited to realize a targeted quantum phase remains a formidable challenge. Beyond tunability, an effective quantum simulator requires guiding design principles that connect microscopic ingredients to emergent behavior.
In this talk, I will describe recent progress toward establishing such back‑engineering design principles for moiré materials. After introducing the architecture of van der Waals stacks, I will show how the single‑particle motion of electrons in these systems can be efficiently predicted, giving rise to a practical dictionary that links the symmetry and chemical composition of individual layers to emergent properties at the moiré scale [2]. Including interactions, I will further illustrate how to identify, within the vast space of experimentally tunable parameters, the operating conditions required to stabilize fragile correlated phases. This approach has led to the observation of phases hosting anyons [3] — quasiparticles with exotic statistics beyond the standard model. These developments raise the prospect that moiré materials could evolve not only as analog quantum simulators, but also as building blocks for digital quantum computers using spatially resolved control techniques such as inhomogeneous gating to trap and manipulate anyons [4].
[1] Kennes, …, Rubio (2021). Moiré heterostructures as a condensed-matter quantum simulator. Nature Physics, 17(2), 155-163.
[2] Nakatsuji, Cano, Crépel (2025). High-throughput discovery of moir\'e homobilayers guided by topology and energetics. arXiv:2512.15851.
[3] Crépel, Fu (2023). Anomalous Hall metal and fractional Chern insulator in twisted transition metal dichalcogenides. PRB, 107(20), L201109.
[4] Crépel, Regnault (2024). Attractive Haldane bilayers for trapping non-Abelian anyons. PRB, 110(11), 115109.