Valentin Crépel

Robust flavor-polarized phases are a striking hallmark of many flat-band moiré materials. In this Letter, we trace the origin of this spontaneous polarization to a lesser-known quantum-geometric quantity: the quantum-geometric dipole. Analogous to how the quantum metric governs the spatial spread of wave packets, we show that the quantum-geometric dipole sets the characteristic size of particle-hole excitations, e.g., magnons in a ferromagnet, which in turn boosts their gap and stiffness. Indeed, the larger the particle-hole separation, the weaker the mutual attraction and the stronger the excitation energy. In topological bands, this energy enhancement admits a lower bound within the local-mode approximation, highlighting the crucial role of topology in flat-band ferromagnetism. We illustrate these effects in microscopic models, emphasizing their generality and relevance to moiré materials. Our results establish the quantum-geometric dipole as a predictive geometric indicator for ferromagnetism in flat bands, a crucial prerequisite for topological order.

Twisted WSe 2 hosts superconductivity, metal-insulator phase transitions, and field-controllable Fermi-liquid to non-Fermi-liquid transport properties. In this work, we use dynamical mean-field theory to provide a coherent understanding of the electronic correlations shaping the twisted WSe 2 phase diagram. We find a correlated metal competing with three distinct site-polarized correlated insulators; the competition is controlled by interlayer potential difference and interaction strength. The insulators are characterized by a strong differentiation between orbitals with respect to carrier concentration and effective correlation strength. Upon doping, a strong particle-hole asymmetry emerges, resulting from a Zaanen-Sawatzky-Allen-type charge-transfer mechanism. The associated charge-transfer physics and proximity to a van Hove singularity in the correlated metal sandwiched between two site-polarized insulators naturally explains the interlayer potential-driven metal-to-insulator transition, particle-hole asymmetry in transport, and the coherence-incoherence crossover in 3 . 65 ∘ twisted WSe 2 .

Symmetry-resolved entanglement entropy provides a powerful framework for probing the internal structure of quantum many-body states by decomposing entanglement into contributions from distinct symmetry sectors. In this work, we apply matrix product state techniques to study the bosonic, non-Abelian Moore-Read quantum Hall state, enabling precise numerical evaluation of both the full counting statistics and symmetry-resolved entanglement entropies. Our results reveal an approximate equipartition of entanglement among symmetry sectors, consistent with theoretical expectations and subject to finite-size corrections. The results also show that these expectations for symmetry-resolved entanglement entropy remain valid in the case of a non-Abelian state where the topological sectors cannot be distinguished by the Abelian U ( 1 ) symmetry alone, and where neutral and charged modes possess distinct velocities. We additionally perform a detailed comparison of the entanglement spectrum with predictions from the Li-Haldane conjecture, finding remarkable agreement, and enabling a more precise understanding of the effects of the distinct neutral and charged velocities. This not only provides a stringent test of the conjecture but also highlights its explanatory power in understanding the origin and structure of finite-size effects across different symmetry sectors.

The recent observation of superconductivity in the vicinity of Fermi surface reconstructed insulating or metallic states has established twisted bilayers of WSe 2 as an exciting platform to study the interplay of strong electron-electron interactions, broken symmetries, and topology. In this work, we use a first-principles, material-specific theoretical treatment that is unbiased with respect to electronic instabilities to study the emergence of electronic ordering in twisted WSe 2 driven by gate-screened Coulomb interactions. We construct exponentially localized moiré Wannier orbitals that faithfully capture the band structure and topology of the system, project the gate-screened Coulomb interaction onto them, and use unbiased functional renormalization group techniques to resolve the momentum and orbital structure of the leading instabilities and the relevant energy scales. We find an interplay between intervalley-coherent antiferromagnetic (IVC-AFM) order and chiral, mixed-parity d / p -wave superconductivity for carrier concentrations near a displacement field and twist-angle-tunable van Hove singularity. Our microscopic approach establishes incommensurate IVC-AFM spin fluctuations as the dominant electronic mechanism driving the formation of superconductivity in θ = 5.08 ° twisted WSe 2 and explains key aspects of recent experiments including the asymmetric density dependence of the spin ordering with respect to the van Hove line, the single- and double-peak structure of the DOS in the ordered (hole-doped) IVC-AFM phase, the emergence of superconductivity as the density is varied across the van Hove line, and the evolution of the displacement field-density phase diagram with twist angles between 3.7 ° … 5 ° . We show that the interplay of electronic correlations and nontrivial quantum geometry in tWSe 2 manifests in orbital-selective order parameters associated to the IVC-AFM and SC states that are detectable by local spectroscopy measurements.

We argue that the combination of strong repulsive interactions and high magnetic fields can generate electron pairing and superconductivity. Inspired by the large lattice constants of moiré materials, which make large flux per unit cell accessible at laboratory fields, we study the triangular lattice Hofstadter–Hubbard model at one-quarter flux quantum per plaquette, where previous literature has argued that a chiral spin liquid separates a weak-coupling integer quantum Hall phase and a strong-coupling topologically trivial antiferromagnetic insulator at a density of one electron per site. We argue that topological superconductivity emerges upon doping in the vicinity of the integer quantum Hall to chiral spin liquid transition. We employ exact diagonalization and density matrix renormalization group methods to examine this theoretical scenario and find that electronic pairing indeed occurs on both sides of criticality over a remarkably broad range of interaction strengths. On the chiral spin liquid side, our results provide a concrete model realization of the long-hypothesized mechanism of anyon superconductivity. Our study thus establishes a beyond-Bardeen-Cooper-Schrieffer route to electron pairing in a well-controlled limit, relying crucially on the interplay between electron correlations and band topology.

The observation of delicate correlated phases in twisted heterostructures of graphene and transition metal dichalcogenides suggests that moiré flat bands are intrinsically resilient against certain types of disorder. Here, we investigate the robustness of moiré flat bands in the chiral limit of the Bistritzer-MacDonald model—applicable to both platforms in certain limits—and demonstrate drastic differences between the first magic angle and higher magic angles in response to chiral symmetric disorder that arise, for instance, from lattice relaxation. We understand these differences using a hidden constant of motion that permits the decomposition of the non-Abelian gauge field induced by interlayer tunnelings into two decoupled Abelian ones. At all magic angles, the resulting effective magnetic field splits into an anomalous contribution and a fluctuating part. The anomalous field maps the moiré flat bands onto a zeroth Dirac Landau level, whose flatness withstands any chiral symmetric perturbation such as nonuniform magnetic fields due to a topological index theorem—thereby underscoring a topological mechanism for band flatness. Only the first magic angle can fully harness this topological protection due to its weak fluctuating magnetic field. In higher magic angles, the amplitude of fluctuations largely exceeds the anomalous contribution, which we find results in a physically meaningless chiral operator and an extremely large sensitivity to microscopic details and an exponential collapse of the single-particle gap. Through numerical simulations, we further study various types of disorder and identify the scattering processes that are enhanced or suppressed in the chiral limit. Interestingly, we find that the topological suppression of disorder broadening persists away from the chiral limit and is further accentuated by isolating a single sublattice polarized flat band in energy. Our analysis suggests the Berry curvature hot spot at the top of the K and K ′ valence band in the transition metal dichalcogenide monolayers is essential for the stability of its moiré flat bands and their correlated states. Published by the American Physical Society 2025

Two-dimensional materials subject to long-wavelength modulations have emerged as novel platforms to study topological and correlated quantum phases. In this article, we develop a versatile and computationally inexpensive method to predict the topological properties of materials subjected to a superlattice potential by combining degenerate perturbation theory with the method of symmetry indicators. In the absence of electronic interactions, our analysis provides a systematic rule to find the Chern number of the superlattice-induced miniband starting from the harmonics of the applied potential and a few material-specific coefficients. Our method also applies to anomalous (interaction-generated) bands, for which we derive an efficient algorithm to determine all Chern numbers compatible with a self-consistent solution to the Hartree-Fock equations. Our approach gives a microscopic understanding of the quantum anomalous Hall insulators recently observed in rhombohedral graphene multilayers.