On-chip multi-degree-of-freedom control of two-dimensional materials.

Two-dimensional materials (2DM) and their heterostructures offer tunable electrical and optical properties, primarily modifiable through electrostatic gating and twisting. Although electrostatic gating is a well-established method for manipulating 2DM, achieving real-time control over interfacial properties remains challenging in exploring 2DM physics and advanced quantum device technology1-6. Current methods, often reliant on scanning microscopes, are limited in their scope of application, lacking the accessibility and scalability of electrostatic gating at the device level. Here we introduce an on-chip platform for 2DM with in situ adjustable interfacial properties, using a microelectromechanical system (MEMS). This platform comprises compact and cost-effective devices with the ability of precise voltage-controlled manipulation of 2DM, including approaching, twisting and pressurizing actions. We demonstrate this technology by creating synthetic topological singularities, such as merons, in the nonlinear optical susceptibility of twisted hexagonal boron nitride (h-BN)7-10. A key application of this technology is the development of integrated light sources with real-time and wide-range tunable polarization. Furthermore, we predict a quantum analogue that can generate entangled photon pairs with adjustable entanglement properties. Our work extends the abilities of existing technologies in manipulating low-dimensional quantum materials and paves the way for new hybrid two- and three-dimensional devices, with promising implications in condensed-matter physics, quantum optics and related fields.

Superconductivity and strong interactions in a tunable moiré quasicrystal.

Electronic states in quasicrystals generally preclude a Bloch description1, rendering them fascinating and enigmatic. Owing to their complexity and scarcity, quasicrystals are underexplored relative to periodic and amorphous structures. Here we introduce a new type of highly tunable quasicrystal easily assembled from periodic components. By twisting three layers of graphene with two different twist angles, we form two mutually incommensurate moiré patterns. In contrast to many common atomic-scale quasicrystals2,3, the quasiperiodicity in our system is defined on moiré length scales of several nanometres. This 'moiré quasicrystal' allows us to tune the chemical potential and thus the electronic system between a periodic-like regime at low energies and a strongly quasiperiodic regime at higher energies, the latter hosting a large density of weakly dispersing states. Notably, in the quasiperiodic regime, we observe superconductivity near a flavour-symmetry-breaking phase transition4,5, the latter indicative of the important role that electronic interactions play in that regime. The prevalence of interacting phenomena in future systems with in situ tunability is not only useful for the study of quasiperiodic systems but may also provide insights into electronic ordering in related periodic moiré crystals6-12. We anticipate that extending this platform to engineer quasicrystals by varying the number of layers and twist angles, and by using different two-dimensional components, will lead to a new family of quantum materials to investigate the properties of strongly interacting quasicrystals.

Moiré synaptic transistor with room-temperature neuromorphic functionality.

Moiré quantum materials host exotic electronic phenomena through enhanced internal Coulomb interactions in twisted two-dimensional heterostructures1-4. When combined with the exceptionally high electrostatic control in atomically thin materials5-8, moiré heterostructures have the potential to enable next-generation electronic devices with unprecedented functionality. However, despite extensive exploration, moiré electronic phenomena have thus far been limited to impractically low cryogenic temperatures9-14, thus precluding real-world applications of moiré quantum materials. Here we report the experimental realization and room-temperature operation of a low-power (20 pW) moiré synaptic transistor based on an asymmetric bilayer graphene/hexagonal boron nitride moiré heterostructure. The asymmetric moiré potential gives rise to robust electronic ratchet states, which enable hysteretic, non-volatile injection of charge carriers that control the conductance of the device. The asymmetric gating in dual-gated moiré heterostructures realizes diverse biorealistic neuromorphic functionalities, such as reconfigurable synaptic responses, spatiotemporal-based tempotrons and Bienenstock-Cooper-Munro input-specific adaptation. In this manner, the moiré synaptic transistor enables efficient compute-in-memory designs and edge hardware accelerators for artificial intelligence and machine learning.

Pauli-limit violation and re-entrant superconductivity in moiré graphene.

Moiré quantum matter has emerged as a materials platform in which correlated and topological phases can be explored with unprecedented control. Among them, magic-angle systems constructed from two or three layers of graphene have shown robust superconducting phases with unconventional characteristics1-5. However, direct evidence of unconventional pairing remains to be experimentally demonstrated. Here we show that magic-angle twisted trilayer graphene exhibits superconductivity up to in-plane magnetic fields in excess of 10 T, which represents a large (2-3 times) violation of the Pauli limit for conventional spin-singlet superconductors6,7. This is an unexpected observation for a system that is not predicted to have strong spin-orbit coupling. The Pauli-limit violation is observed over the entire superconducting phase, which indicates that it is not related to a possible pseudogap phase with large superconducting amplitude pairing. Notably, we observe re-entrant superconductivity at large magnetic fields, which is present over a narrower range of carrier densities and displacement fields. These findings suggest that the superconductivity in magic-angle twisted trilayer graphene is likely to be driven by a mechanism that results in non-spin-singlet Cooper pairs, and that the external magnetic field can cause transitions between phases with potentially different order parameters. Our results demonstrate the richness of moiré superconductivity and could lead to the design of next-generation exotic quantum matter.

Flavour Hund's coupling, Chern gaps and charge diffusivity in moiré graphene.

Interaction-driven spontaneous symmetry breaking lies at the heart of many quantum phases of matter. In moiré systems, broken spin/valley 'flavour' symmetry in flat bands underlies the parent state from which correlated and topological ground states ultimately emerge1-10. However, the microscopic mechanism of such flavour symmetry breaking and its connection to the low-temperature phases are not yet understood. Here we investigate the broken-symmetry many-body ground state of magic-angle twisted bilayer graphene (MATBG) and its nontrivial topology using simultaneous thermodynamic and transport measurements. We directly observe flavour symmetry breaking as pinning of the chemical potential at all integer fillings of the moiré superlattice, demonstrating the importance of flavour Hund's coupling in the many-body ground state. The topological nature of the underlying flat bands is manifested upon breaking time-reversal symmetry, where we measure energy gaps corresponding to Chern insulator states with Chern numbers 3, 2, 1 at filling factors 1, 2, 3, respectively, consistent with flavour symmetry breaking in the Hofstadter butterfly spectrum of MATBG. Moreover, concurrent measurements of resistivity and chemical potential provide the temperature-dependent charge diffusivity of MATBG in the strange-metal regime11-a quantity previously explored only in ultracold atoms12. Our results bring us one step closer to a unified framework for understanding interactions in the topological bands of MATBG, with and without a magnetic field.

Tunable strongly coupled superconductivity in magic-angle twisted trilayer graphene.

Moiré superlattices1,2 have recently emerged as a platform upon which correlated physics and superconductivity can be studied with unprecedented tunability3-6. Although correlated effects have been observed in several other moiré systems7-17, magic-angle twisted bilayer graphene remains the only one in which robust superconductivity has been reproducibly measured4-6. Here we realize a moiré superconductor in magic-angle twisted trilayer graphene (MATTG)18, which has better tunability of its electronic structure and superconducting properties than magic-angle twisted bilayer graphene. Measurements of the Hall effect and quantum oscillations as a function of density and electric field enable us to determine the tunable phase boundaries of the system in the normal metallic state. Zero-magnetic-field resistivity measurements reveal that the existence of superconductivity is intimately connected to the broken-symmetry phase that emerges from two carriers per moiré unit cell. We find that the superconducting phase is suppressed and bounded at the Van Hove singularities that partially surround the broken-symmetry phase, which is difficult to reconcile with weak-coupling Bardeen-Cooper-Schrieffer theory. Moreover, the extensive in situ tunability of our system allows us to reach the ultrastrong-coupling regime, characterized by a Ginzburg-Landau coherence length that reaches the average inter-particle distance, and very large TBKT/TF values, in excess of 0.1 (where TBKT and TF are the Berezinskii-Kosterlitz-Thouless transition and Fermi temperatures, respectively). These observations suggest that MATTG can be electrically tuned close to the crossover to a two-dimensional Bose-Einstein condensate. Our results establish a family of tunable moiré superconductors that have the potential to revolutionize our fundamental understanding of and the applications for strongly coupled superconductivity.

Entropic evidence for a Pomeranchuk effect in magic-angle graphene.

In the 1950s, Pomeranchuk1 predicted that, counterintuitively, liquid 3He may solidify on heating. This effect arises owing to high excess nuclear spin entropy in the solid phase, where the atoms are spatially localized. Here we find that an analogous effect occurs in magic-angle twisted bilayer graphene2-6. Using both local and global electronic entropy measurements, we show that near a filling of one electron per moiré unit cell, there is a marked increase in the electronic entropy to about 1kB per unit cell (kB is the Boltzmann constant). This large excess entropy is quenched by an in-plane magnetic field, pointing to its magnetic origin. A sharp drop in the compressibility as a function of the electron density, associated with a reset of the Fermi level back to the vicinity of the Dirac point, marks a clear boundary between two phases. We map this jump as a function of electron density, temperature and magnetic field. This reveals a phase diagram that is consistent with a Pomeranchuk-like temperature- and field-driven transition from a low-entropy electronic liquid to a high-entropy correlated state with nearly free magnetic moments. The correlated state features an unusual combination of seemingly contradictory properties, some associated with itinerant electrons-such as the absence of a thermodynamic gap, metallicity and a Dirac-like compressibility-and others associated with localized moments, such as a large entropy and its disappearance under a magnetic field. Moreover, the energy scales characterizing these two sets of properties are very different: whereas the compressibility jump has an onset at a temperature of about 30 kelvin, the bandwidth of magnetic excitations is about 3 kelvin or smaller. The hybrid nature of the present correlated state and the large separation of energy scales have implications for the thermodynamic and transport properties of the correlated states in twisted bilayer graphene.

Fractional Chern insulators in magic-angle twisted bilayer graphene.

Fractional Chern insulators (FCIs) are lattice analogues of fractional quantum Hall states that may provide a new avenue towards manipulating non-Abelian excitations. Early theoretical studies1-7 have predicted their existence in systems with flat Chern bands and highlighted the critical role of a particular quantum geometry. However, FCI states have been observed only in Bernal-stacked bilayer graphene (BLG) aligned with hexagonal boron nitride (hBN)8, in which a very large magnetic field is responsible for the existence of the Chern bands, precluding the realization of FCIs at zero field. By contrast, magic-angle twisted BLG9-12 supports flat Chern bands at zero magnetic field13-17, and therefore offers a promising route towards stabilizing zero-field FCIs. Here we report the observation of eight FCI states at low magnetic field in magic-angle twisted BLG enabled by high-resolution local compressibility measurements. The first of these states emerge at 5 T, and their appearance is accompanied by the simultaneous disappearance of nearby topologically trivial charge density wave states. We demonstrate that, unlike the case of the BLG/hBN platform, the principal role of the weak magnetic field is merely to redistribute the Berry curvature of the native Chern bands and thereby realize a quantum geometry favourable for the emergence of FCIs. Our findings strongly suggest that FCIs may be realized at zero magnetic field and pave the way for the exploration and manipulation of anyonic excitations in flat moiré Chern bands.

Tunable correlated states and spin-polarized phases in twisted bilayer-bilayer graphene.

The recent discovery of correlated insulator states and superconductivity in magic-angle twisted bilayer graphene1,2 has enabled the experimental investigation of electronic correlations in tunable flat-band systems realized in twisted van der Waals heterostructures3-6. This novel twist angle degree of freedom and control should be generalizable to other two-dimensional systems, which may exhibit similar correlated physics behaviour, and could enable techniques to tune and control the strength of electron-electron interactions. Here we report a highly tunable correlated system based on small-angle twisted bilayer-bilayer graphene (TBBG), consisting of two rotated sheets of Bernal-stacked bilayer graphene. We find that TBBG exhibits a rich phase diagram, with tunable correlated insulator states that are highly sensitive to both the twist angle and the application of an electric displacement field, the latter reflecting the inherent polarizability of Bernal-stacked bilayer graphene7,8. The correlated insulator states can be switched on and off by the displacement field at all integer electron fillings of the moiré unit cell. The response of these correlated states to magnetic fields suggests evidence of spin-polarized ground states, in stark contrast to magic-angle twisted bilayer graphene. Furthermore, in the regime of lower twist angles, TBBG shows multiple sets of flat bands near charge neutrality, resulting in numerous correlated states corresponding to half-filling of each of these flat bands, all of which are tunable by the displacement field as well. Our results could enable the exploration of twist-angle- and electric-field-controlled correlated phases of matter in multi-flat-band twisted superlattices.

Author Correction: Tunable correlated states and spin-polarized phases in twisted bilayer-bilayer graphene.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.