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Magnetism in Moiré Materials
This project focused on the theory of the electronic properties of magnetic moire materials. Moire materials can be formed by overlaying two or more two-dimensional crystals that are either semiconductors or semimetals and establishing a moire pattern. Low-energy electronic properties are then described by a continuum model with crystalline periodicity. Moire materials are therefore artificial two-dimensional crys- tals whose periodicity is at the tens of nanometers scale, increasing the unit cell area by a factor of about 10,000 compared to real crystals. They are important because the main tuning knob of chemistry, the number of electrons per effective atom or molecule (the analog of the number of electrons per unit cell in real crystals), can be shifted by more than one simply by using electrical gates. The research covered two diffeerent classes of moire materials, graphene multilayers twisted to a rotation angle at which correlations are strong, and transition metal dichalcogenide semiconductors. The proposal identifed one project in each area both related very broadly to magnetism: i) Advancing understanding of broken spin-valley and sublattice symmetries in Magic Angle Twisted Bilayer Graphene and ii) Developing the theory of itinerant electron magnetism in Gamma-valley and K-valley transition metal dichalcogenide moire materials.
Evidence for unconventional superconductivity in twisted bilayer graphene
The emergence of superconductivity and correlated insulators in magic-angle twisted bilayer graphene (MATBG) has raised the intriguing possibility that its pairing mechanism is distinct from that of conventional superconductors, as described by the Bardeen–Cooper–Schrieffer (BCS) theory. However, recent studies have shown that superconductivity persists even when Coulomb interactions are partially screened5. This suggests that pairing in MATBG might be conventional in nature and a consequence of the large density of states of its flat bands. In this work, we combine tunnelling and Andreev reflection spectroscopy with a scanning tunnelling microscope to observe several key experimental signatures of unconventional superconductivity in MATBG. We show that the tunnelling spectra below the transition temperature T c are inconsistent with those of a conventional s-wave superconductor, but rather resemble those of a nodal superconductor with an anisotropic pairing mechanism. We observe a large discrepancy between the tunnelling gap Δ T , which far exceeds the mean-field BCS ratio (with 2Δ T /k B T c ~ 25), and the gap Δ AR extracted from Andreev reflection spectroscopy (2Δ AR /k B T c ~ 6). The tunnelling gap persists even when superconductivity is suppressed, indicating its emergence from a pseudogap phase. Moreover, the pseudogap and superconductivity are both absent when MATBG is aligned with hexagonal boron nitride. These findings and other observations reported here provide a preponderance of evidence for a non-BCS mechanism for superconductivity in MATBG.
Strain-Induced Growth of Twisted Bilayers during the Coalescence of Monolayer MoS 2 Crystals
Tailoring the grain boundaries (GBs) and twist angles between two-dimensional (2D) crystals are two crucial synthetic challenges to deterministically enable envisioned applications such as moiré excitons, emerging magnetism, or single-photon emission. Here, we reveal how twisted 2D bilayers can be synthesized from the collision and coalescence of two growing monolayer MoS 2 crystals during chemical vapor deposition. The twisted bilayer (TB) moiré angles are found to preserve the misorientation angle (θ) of the colliding crystals. The shapes of the TB regions are rationalized by a kink propagation model that predicts the GB formed by the coalescing crystals. Optical spectroscopy measurements reveal a θ-dependent long-range strain in crystals with stitched grain boundaries and a sharp (θ > 20°) threshold for the appearance of TBs, which relieves this strain. Reactive molecular dynamics simulations explain this strain from the continued growth of the crystals during coalescence due to the insertion of atoms at unsaturated defects along the GB, a process that self-terminates when the defects become saturated. The simulations also reproduce atomic-resolution electron microscopy observations of faceting along the GB, which is shown to arise from the growth-induced long-range strain. These facets align with the axes of the colliding crystals to provide favorable nucleation sites for second-layer growth of a TB with twist angles that preserve the misorientation angle θ. This interplay between strain generation and aligned nucleation provides a synthetic pathway for the growth of TBs with deterministic angles.
Competing Zero-Field Chern Insulators in Superconducting Twisted Bilayer Graphene
The discovery of magic angle twisted bilayer graphene has unveiled a rich variety of superconducting, magnetic, and topologically nontrivial phases. Here, we show that the zero-field states at odd integer filling factors in h-BN nonaligned devices are consistent with symmetry broken Chern insulators, as is evidenced by the observation of the anomalous Hall effect near moiré cell filling factor ν = +1. The corresponding Chern insulator has a Chern number C = ±1 and a relatively high Curie temperature of T c ≈ 4.5 K. In a perpendicular magnetic field above B > 0.5 T we observe a transition of the ν = +1 Chern insulator from Chern number C = ±1 to C = 3, characterized by a quantized Hall plateau with R yx = h/3e 2 . These observations demonstrate that interaction-induced symmetry breaking leads to zero-field ground states that include almost degenerate and closely competing Chern insulators, and that states with larger Chern numbers couple most strongly to the B field. In addition, the device reveals strong superconducting phases with critical temperatures of up to T c ≈ 3.5 K. By providing the first demonstration of a system that allows gate-induced transitions between magnetic and superconducting phases, our observations mark a major milestone in the creation of a new generation of quantum electronics.
Moiréless correlations in ABCA graphene
Atomically thin van der Waals materials stacked with an interlayer twist have proven to be an excellent platform toward achieving gate-tunable correlated phenomena linked to the formation of flat electronic bands. In this work we demonstrate the formation of emergent correlated phases in multilayer rhombohedral graphene––a simple material that also exhibits a flat electronic band edge but without the need of having a moiré superlattice induced by twisted van der Waals layers. We show that two layers of bilayer graphene that are twisted by an arbitrary tiny angle host large (micrometer-scale) regions of uniform rhombohedral four-layer (ABCA) graphene that can be independently studied. Scanning tunneling spectroscopy reveals that ABCA graphene hosts an unprecedentedly sharp van Hove singularity of 3–5-meV half-width. We demonstrate that when this van Hove singularity straddles the Fermi level, a correlated many-body gap emerges with peak-to-peak value of 9.5 meV at charge neutrality. Mean-field theoretical calculations for model with short-ranged interactions indicate that two primary candidates for the appearance of this broken symmetry state are a charge-transfer excitonic insulator and a ferrimagnet. Finally, we show that ABCA graphene hosts surface topological helical edge states at natural interfaces with ABAB graphene which can be turned on and off with gate voltage, implying that small-angle twisted double-bilayer graphene is an ideal programmable topological quantum material.
Anisotropic Raman Scattering and Lattice Orientation Identification of 2M-WS 2
Anisotropic materials with low symmetries hold significant promise for next-generation electronic and quantum devices. 2M-WS 2 , which is a candidate for topological superconductivity, has garnered considerable interest. However, a comprehensive understanding of how its anisotropic features contribute to unconventional superconductivity, along with a simple, reliable method to identify its crystal orientation, remains elusive. Here, we combine theoretical and experimental approaches to investigate angle- and polarization-dependent anisotropic Raman modes of 2M-WS 2 . Through first-principles calculations, we predict and analyze the phonon dispersion and lattice vibrations of all Raman modes in 2M-WS 2 . We establish a direct correlation between their anisotropic Raman spectra and high-resolution transmission electron microscopy images. Finally, we demonstrate that anisotropic Raman spectroscopy can accurately determine the crystal orientation and twist angle between two stacked 2M-WS 2 layers. Furthermore, our findings provide insights into the electron–phonon coupling and anisotropic properties of 2M-WS 2 , paving the way for the use of anisotropic materials in advanced electronic and quantum devices.
A New Platform for Twistronics: Perovskite Moiré Superlattices Beyond van der Waals
Moiré superlattices have reshaped condensed‐matter physics by enabling twist‐angle engineering of electronic and excitonic states, traditionally in van der Waals (vdW) systems. This Perspective focuses on perovskites as a transformative non‐van der Waals (non‐vdW) platform for twistronics. These materials are distinguished by ionic‐covalent bonding and soft octahedral lattices that support deep moiré potentials (≈100–200 meV), which in turn yield bright, room‐temperature excitons and tunable quantum phenomena. We organize recent advances into two core classes: (i) moiré superlattices constructed from 2D Ruddlesden‐Popper (RP) perovskites via spontaneous or guided twisted stacking; and (ii) moiré architectures in 3D perovskite lamellae, achieved through topotactic 2D RP‐to‐3D conversion and ligand‐induced self‐assembly. Key experimental observations in these systems include twist‐tunable moiré periods, suppressed exciton–exciton annihilation, flat band‐like transport, and ferroelectric vortex lattices in their oxide perovskite counterparts. Here, we outline key bottlenecks, including defects arising during phase conversion, stringent lattice‐matching requirements, and the absence of in situ twist metrology, and highlight opportunities in lattice‐mismatched heterostructures and multifunctional quantum‐optoelectronic devices. Collectively, these advances establish perovskite moiré systems as a critical bridge between fundamental moiré physics and room‐temperature technological applications.
Twistronics of Janus transition metal dichalcogenide bilayers
Twisted multilayers of two-dimensional (2D) materials are an increasingly important platform for investigating quantum phases of matter, and in particular, strongly correlated electrons. The moiré pattern introduced by the relative twist between layers creates effective potentials of long wavelength, leading to electron localization. However, in contrast to the abundance of 2D materials, few twisted heterostructures have been studied until now. Here, in this study, we develop a first-principles continuum theory to study the electronic bands introduced by moire patterns of twisted Janus transition metal dichalcogenide (TMD) homo- and heterobilayers. The model includes lattice relaxation, stacking-dependent effective mass, and Rashba spin-orbit coupling. We then perform a high-throughput generation and characterization of DFT-extracted continuum models for more than a hundred possible combinations of materials and stackings. Our model predicts that the moiré physics and emergent symmetries depend on chemical composition, vertical layer orientation, and twist angle, so that the miniband wave functions can form triangular, honeycomb, and kagome networks. Rashba spin-orbit effects, peculiar of these systems, can dominate the moiré bandwidth at small angles. Our work enables detailed investigation of Janus twisted heterostructures, allowing the discovery and control of novel electronic phenomena.
Trions in twisted bilayer graphene
The strong-coupling phase diagram of magic-angle twisted bilayer graphene (TBG) predicts a series of exact one-particle charge ±1 gapped excitations on top of the integer-filled ferromagnetic ground states. Finite-size exact diagonalization studies showed that these are the lowest charge ±1 excitations in the system (for 10 nm screening length), with the exception of charge +1 at filling -1 in the chiral limit. In the current paper we show that this “trion bound state,” a 3-particle, charge 1 excitation of the insulating ferromagnetic ground state of the projected Hamiltonian of TBG, is the lowest charge +1 overall excitation at ν =-1, and also for some large (≈20 nm) screening lengths at ν =-2 in the chiral limit and with very small binding energy. At other fillings, we show that trion bound states do exist, but only for momentum ranges that do not cover the entire moiré Brillouin zone. The trion bound states (at different momenta) exist for finite parameter range w 0 /w 1 but they all disappear in the continuum far below the realistic values of w 0 /w 1 = 0.8. Thus we find the conditions for the existence of the trion bound state, a good variational wave function for it, and investigate its behavior for different screening lengths, at all integer fillings, on both the electron and hole sides.
Spin magnetometry as a probe of stripe superconductivity in twisted bilayer graphene
The discovery of alternating superconducting and insulating ground states in magic angle graphene has suggested an intriguing analogy with cuprate high-T c materials. In this paper we argue that the network states of small angle twisted bilayer graphene (TBG) afford a further perspective on the cuprates by emulating their stripe-ordered phases, as in La 1.875 Ba 0.125 CuO 4 . We show that the spin and valley quantum numbers of stripes in TBG graphene fractionalize, developing characteristic signatures in the tunneling density of states and the magnetic noise spectrum of impurity spins. By examining the coupling between the charge rivers we determine the superconducting transition temperature. Our study suggests that twisted bilayer graphene can be used for a controlled emulation of stripe superconductivity and quantum sensing experiments of emergent anyonic excitations.
Impurity effects on local electronic structure of twisted bilayer cuprates
It has been recently proposed that a fully gapped d-wave superconducting phase emerges in twisted bilayer cuprates when twist angle is in the vicinity of 45°. By considering a twisted bilayer model with a moiré cell, we study the local electronic structure around a single-site impurity and impurity dimer in both topologically trivial and nontrivial superconducting states. Here we find that the topological nontrivial superconducting phase is robust against single scalar-potential impurity scattering but is very sensitive to the interlayer impurity dimer scattering, which avoids and enforces the creation of the subgap quasiparticle state. This behavior is intrinsic to the bilayer structure and topological nature, in contrast to the other types of impurities that inevitably bring subgap quasiparticle states. We expect that our results can contribute to the understanding of electronic properties of twisted bilayer cuprates systems.
Reentrant superconductivity through a quantum Lifshitz transition in twisted trilayer graphene
A series of recent experiments has demonstrated robust superconductivity in magic-angle twisted trilayer graphene (TTG). In particular, a recent work by Cao et al. [Nature (London) 595, 526 (2021)] studies the behavior of the superconductor in an in-plane magnetic field and an out-of-plane displacement field, finding that the superconductor is unlikely to have purely spin-singlet pairing. Herein, this work also finds that at high magnetic fields and a smaller range of dopings and displacement fields, the superconductor undergoes a transition to a distinct field-induced superconducting state. Inspired by these results, we develop an understanding of the superconductivity in TTG using a combination of phenomenological reasoning and microscopic theory. We describe the role that an in-plane field plays in TTG, and we use this understanding to argue that the reentrant transition may be associated with a quantum Lifshitz phase transition, with the high-field phase possessing finite-momentum pairing. We argue that the superconductor is likely to involve a superposition of singlet and triplet pairing, and we describe the structure of the normal state. We also draw lessons for twisted bilayer graphene (TBG), and we explain the differences in the phenomenology with TTG despite their close microscopic relationship. We propose that a singlet-triplet superposition is realized in the TBG superconductor as well, and that the ν = –2 correlated insulator may be a time-reversal protected Z 2 topological insulator obtained through spontaneous spin symmetry breaking.
Design of Twisted Two-Dimensional Heterostructures and Performance Regulation Descriptor for Electrocatalytic Ammonia Production from Nitric Oxide
The electrocatalytic reduction of nitric oxide (NO) to ammonia (NH 3 ) represents an attractive alternative for valorizing waste NO streams (NORR). However, discovering efficient catalysts for NO-to-NH 3 conversion remains challenging. We have designed metal-intercalated twisted graphene-BN heterostructures, in which metal atoms act as electron-transfer bridges. The twisted configuration facilitates cross-interface charge transfer, redistributing electrons from the graphene–metal interface to the metal–BN interface and BN surface. This electronic modulation enables boron atom adjacent to the metal center in BN to serve as active sites, promoting strong chemisorption and enhanced activation of NO. After high-throughput screening of the stability and NO capture ability of various transition metal-intercalated twisted heterostructures, we have investigated systematically the NORR pathways across 30 candidates. The results show that the rBN-Ti-Gθ and rBN-V-Gθ heterostructures exhibit exceptional NO-to-NH 3 catalytic performance under optimized twisting conditions. Additionally, using sure independence screening and sparsifying operator (SISSO) for model training, we propose a descriptor and establish a relationship between the twist angle and catalytic activity. This study bridges the gap in applying twisted heterostructures to NORR electrocatalysis and provides new insights and strategies for designing high-performance NORR catalysts.
Twisted symmetric trilayer graphene. II. Projected Hartree-Fock study
The Hamiltonian of the magic-angle twisted symmetric trilayer graphene (TSTG) can be decomposed into a twisted-bilayer-graphene- (TBG-) like flat band Hamiltonian and a high-velocity Dirac fermion Hamiltonian. We use Hartree-Fock mean field approach to study the projected Coulomb interacting Hamiltonian of TSTG developed in Calugaru et al. [Phys. Rev. B 103, 195411 (2021)] at integer fillings ν = -3, -2, -1, and 0 measured from charge neutrality. We study the phase diagram with w 0 /w 1 , the ratio of AA and AB interlayer hoppings, and the displacement field, which introduces an interlayer potential U and hybridizes the TBG-like bands with the Dirac bands. At small U, we find the ground states at all fillings ν are in the same phases as the tensor products of a Dirac semimetal with the filling ν TBG insulator ground states, which are spin-valley polarized at ν = -3, and fully (partially) intervalley coherent at ν = -2, 0(ν = -1) in the flat bands. An exception is ν = -3 with w 0 /w 1 ≳ 0.7 , which possibly becomes a metal with competing orders at small U due to charge transfers between the Dirac and flat bands. At strong U where the bandwidths exceed interactions, all the fillings ν enter a metal phase with small or zero valley polarization and intervalley coherence. Lastly, at intermediate U, semimetal or insulator phases with zero intervalley coherence may arise for ν = -2, -1, 0. Finally, our results provide a simple picture for the electron interactions in TSTG systems, and reveal the connection between the TSTG and TBG ground states.
Unidirectional ray polaritons in twisted asymmetric stacks
Abstract The vast repository of van der Waals (vdW) materials supporting polaritons offers numerous possibilities to tailor electromagnetic waves at the nanoscale. The development of twistoptics—the modulation of the optical properties by twisting stacks of vdW materials—enables directional propagation of phonon polaritons (PhPs) along a single spatial direction, known as canalization. Here we demonstrate a complementary type of directional propagation of polaritons by reporting the visualization of unidirectional ray polaritons (URPs). They arise naturally in twisted hyperbolic stacks with very different thicknesses of their constituents, demonstrated for homostructures of$$\alpha$$ α -MoO 3 and heterostructures of$$\alpha$$ α -MoO 3 and$$\beta$$ β -Ga 2 O 3 . Importantly, their ray-like propagation, characterized by large momenta and constant phase, is tunable by both the twist angle and the illumination frequency. Apart from their fundamental importance, our findings introduce twisted asymmetric stacks as efficient platforms for nanoscale directional polariton propagation, opening the door for applications in nanoimaging, (bio)-sensing, or polaritonic thermal management.
Insulators at fractional fillings in twisted bilayer graphene partially aligned to hexagonal boron nitride
At partial fillings of its flat electronic bands, magic-angle twisted bilayer graphene (MATBG) hosts a rich variety of competing correlated phases that show sample-to-sample variations. Divergent phase diagrams in MATBG are often attributed to the sublattice polarization energy scale, tuned by the degree of alignment of the hexagonal boron nitride (hBN) substrates typically used in van der Waals devices. Unaligned MATBG exhibits unconventional superconductor and correlated insulator phases, while nearly perfectly aligned MATBG/hBN exhibits zero-field Chern insulating phases and lacks superconductivity. Here we use scanning tunneling microscopy and spectroscopy (STM/STS) to observe gapped phases at partial fillings of the flat bands of MATBG in a new intermediate regime of sublattice polarization, observed when MATBG is only partially aligned (θ Gr-hBN ≈ 1.65°) to the underlying hBN substrate. Under this condition, MATBG hosts not only phenomena that naturally interpolate between the two sublattice potential limits, but also unexpected gapped phases absent in either of these limits. At charge neutrality, we observe an insulating phase with a small energy gap (Δ < 5 meV) likely related to weak sublattice symmetry breaking from the hBN substrate. In addition, we observe new gapped phases near fractional fillings ν = ±1/3 and ν = ±1/6, which have not been previously observed in MATBG. Importantly, energy-resolved STS unambiguously identifies these fractional filling states to be of single-particle origin, possibly a result of the super-superlattice formed by two moiré superlattices. Finally, our observations emphasize the power of STS in distinguishing single-particle gapped phases from many-body gapped phases in situations that could be easily confused in electrical transport measurements, and demonstrate the use of substrate engineering for modifying the electronic structure of a moiré flat-band material.