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.

Highly tunable junctions and non-local Josephson effect in magic-angle graphene tunnelling devices.

Magic-angle twisted bilayer graphene (MATBG) has recently emerged as a highly tunable two-dimensional material platform exhibiting a wide range of phases, such as metal, insulator and superconductor states. Local electrostatic control over these phases may enable the creation of versatile quantum devices that were previously not achievable in other single-material platforms. Here we engineer Josephson junctions and tunnelling transistors in MATBG, solely defined by electrostatic gates. Our multi-gated device geometry offers independent control of the weak link, barriers and tunnelling electrodes. These purely two-dimensional MATBG Josephson junctions exhibit non-local electrodynamics in a magnetic field, in agreement with the Pearl theory for ultrathin superconductors. Utilizing the intrinsic bandgaps of MATBG, we also demonstrate monolithic edge tunnelling spectroscopy within the same MATBG devices and measure the energy spectrum of MATBG in the superconducting phase. Furthermore, by inducing a double-barrier geometry, the devices can be operated as a single-electron transistor, exhibiting Coulomb blockade. With versatile functionality encompassed within a single material, these MATBG tunnelling devices may find applications in graphene-based tunable superconducting qubits, on-chip superconducting circuits and electromagnetic sensing.

Nematicity and competing orders in superconducting magic-angle graphene.

Strongly interacting electrons in solid-state systems often display multiple broken symmetries in the ground state. The interplay between different order parameters can give rise to a rich phase diagram. We report on the identification of intertwined phases with broken rotational symmetry in magic-angle twisted bilayer graphene (TBG). Using transverse resistance measurements, we find a strongly anisotropic phase located in a "wedge" above the underdoped region of the superconducting dome. Upon its crossing with the superconducting dome, a reduction of the critical temperature is observed. Furthermore, the superconducting state exhibits an anisotropic response to a direction-dependent in-plane magnetic field, revealing nematic ordering across the entire superconducting dome. These results indicate that nematic fluctuations might play an important role in the low-temperature phases of magic-angle TBG.

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.

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.

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.

Deep-Learning-Enabled Fast Optical Identification and Characterization of 2D Materials.

Advanced microscopy and/or spectroscopy tools play indispensable roles in nanoscience and nanotechnology research, as they provide rich information about material processes and properties. However, the interpretation of imaging data heavily relies on the "intuition" of experienced researchers. As a result, many of the deep graphical features obtained through these tools are often unused because of difficulties in processing the data and finding the correlations. Such challenges can be well addressed by deep learning. In this work, the optical characterization of 2D materials is used as a case study, and a neural-network-based algorithm is demonstrated for the material and thickness identification of 2D materials with high prediction accuracy and real-time processing capability. Further analysis shows that the trained network can extract deep graphical features such as contrast, color, edges, shapes, flake sizes, and their distributions, based on which an ensemble approach is developed to predict the most relevant physical properties of 2D materials. Finally, a transfer learning technique is applied to adapt the pretrained network to other optical identification applications. This artificial-intelligence-based material characterization approach is a powerful tool that would speed up the preparation, initial characterization of 2D materials and other nanomaterials, and potentially accelerate new material discoveries.

Strange Metal in Magic-Angle Graphene with near Planckian Dissipation.

Recent experiments on magic-angle twisted bilayer graphene have discovered correlated insulating behavior and superconductivity at a fractional filling of an isolated narrow band. Here we show that magic-angle bilayer graphene exhibits another hallmark of strongly correlated systems-a broad regime of T-linear resistivity above a small density-dependent crossover temperature-for a range of fillings near the correlated insulator. This behavior is reminiscent of similar behavior in other strongly correlated systems, often denoted "strange metals," such as cuprates, iron pnictides, ruthenates, and cobaltates, where the observations are at odds with expectations in a weakly interacting Fermi liquid. We also extract a transport "scattering rate," which satisfies a near Planckian form that is universally related to the ratio of (k_{B}T/ℏ). Our results establish magic-angle bilayer graphene as a highly tunable platform to investigate strange metal behavior, which could shed light on this mysterious ubiquitous phase of correlated matter.

Phonon Polaritons in Monolayers of Hexagonal Boron Nitride.

Phonon polaritons in van der Waals materials reveal significant confinement accompanied with long propagation length: important virtues for tasks pertaining to the control of light and energy flow at the nanoscale. While previous studies of phonon polaritons have relied on relatively thick samples, here reported is the first observation of surface phonon polaritons in single atomic layers and bilayers of hexagonal boron nitride (hBN). Using antenna-based near-field microscopy, propagating surface phonon polaritons in mono- and bilayer hBN microcrystals are imaged. Phonon polaritons in monolayer hBN are confined in a volume about one million times smaller than the free-space photons. Both the polariton dispersion and their wavelength-thickness scaling law are altered compared to those of hBN bulk counterparts. These changes are attributed to phonon hardening in monolayer-thick crystals. The data reported here have bearing on applications of polaritons in metasurfaces and ultrathin optical elements.

Coherent control of a hybrid superconducting circuit made with graphene-based van der Waals heterostructures.

Quantum coherence and control is foundational to the science and engineering of quantum systems1,2. In van der Waals materials, the collective coherent behaviour of carriers has been probed successfully by transport measurements3-6. However, temporal coherence and control, as exemplified by manipulating a single quantum degree of freedom, remains to be verified. Here we demonstrate such coherence and control of a superconducting circuit incorporating graphene-based Josephson junctions. Furthermore, we show that this device can be operated as a voltage-tunable transmon qubit7-9, whose spectrum reflects the electronic properties of massless Dirac fermions travelling ballistically4,5. In addition to the potential for advancing extensible quantum computing technology, our results represent a new approach to studying van der Waals materials using microwave photons in coherent quantum circuits.