Abstract: When two-dimensional materials are stacked with a relative twist, an emergent moiré translation symmetry reshapes their low-energy electronic structure, giving rise to qualitatively new phases of matter. In recent years, moiré materials have emerged as highly tunable platforms for exploring strong electronic correlations, enabling controlled realizations of many paradigmatic models of condensed matter physics within engineered heterostructures.
In the first part of this talk, I focus on twisted bilayer graphene and show that its correlated electronic states can be naturally understood through a mapping to a topological heavy-fermion model. In this description, localized, strongly correlated f-like electrons coexist with itinerant c-electrons, providing a unified framework for resolving several longstanding experimental puzzles. This perspective allows for a direct computation of the electronic spectral function, now accessible via quantum twisting microscopy, and leads to clear experimental signatures of the emergent coexistence of two electronic species, including a distinctive thermoelectric response [1].
Motivated by the remarkable diversity of correlated phases obtained from a small set of monolayer materials with low-energy states near the K points of the Brillouin zone, the second part of the talk introduces a new class of moiré systems based on triangular-lattice monolayers with low-energy states at the M points [2]. These so-called M-point moiré materials host three time-reversal-preserving valleys related by threefold rotational symmetry. Building on extended ab initio calculations, I show that these systems exhibit projective symmetries leading to quasi-one-dimensional physics, admit analytical strong-coupling descriptions at integer fillings [3], and—remarkably—are free of the sign problem in quantum Monte Carlo simulations at any filling [4]. As a result, they provide an unbiased theoretical platform for studying interaction-driven phenomena. Over experimentally realistic ranges of twist angle and interaction strength, these systems display rich phase diagrams featuring correlated insulators at integer fillings and Wigner–Mott insulating phases at selected commensurate fillings.
[1] D. Călugăru, H. Hu, et al., arXiv:2402.14057
[2] D. Călugăru, Y. Jiang, H. Hu, H. Pi, et al., Nature 643, 376–381 (2025)
[3] M.-R. Li, D. Călugăru, Y. Jiang, H. Pi, et al., arXiv:2508.10098
[4] D. Călugăru, K. Vasiliou, ..., S. A. Parameswaran, In preparation