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Charge distribution offers a unique fingerprint of important properties of electronic systems, including dielectric response, charge ordering, and charge fractionalization. We develop an architecture for charge sensing in two-dimensional electronic systems in a strong magnetic field. We probe local change of the chemical potential in a proximitized detector layer using scanning tunneling microscopy, allowing us to infer the chemical potential and the charge profile in the sample. Our technique has both high energy (<0.3 meV) and spatial (<10 nm) resolution exceeding that of previous studies by an order of magnitude. We apply our technique to study the chemical potential of quantum Hall liquids in monolayer graphene under high magnetic fields and their responses to charge impurities. The chemical potential measurement provides a local probe of the thermodynamic gap of quantum Hall ferromagnets and fractional quantum Hall states. The screening charge profile reveals spatially oscillatory response of the quantum Hall liquids to charge impurities and is consistent with the composite Fermi liquid picture close to the half-filling. Our technique also paves the way to map moiré potentials, probe Wigner crystals, and investigate fractional charges in quantum Hall and Chern insulators. 

Contemporary quantum materials research is guided by themes of topology and electronic correlations. A confluence of these two themes is engineered in moiré materials, an emerging class of highly tunable, strongly correlated 2D materials designed by the rotational or lattice misalignment of atomically thin crystals. In moiré materials, dominant Coulomb interactions among electrons give rise to collective electronic phases, often with robust topological properties. Identifying the mechanisms responsible for these exotic phases is fundamental to our understanding of strongly interacting quantum systems and to our ability to engineer new material properties for potential future technological applications. In this Review, we highlight the contributions of local spectroscopic, thermodynamic and electromagnetic probes to the budding field of moiré materials research. These techniques have not only identified many of the underlying mechanisms of the correlated insulators, generalized Wigner crystals, unconventional superconductors, moiré ferroelectrics and topological orbital ferromagnets found in moiré materials, but have also uncovered fragile quantum phases that have evaded spatially averaged global probes. Furthermore, we highlight recently developed local probe techniques, including local charge sensing and quantum interference probes, that have uncovered new physical observables in moiré materials. 

Wigner predicted that when the Coulomb interactions between electrons become much stronger than their kinetic energy, electrons crystallize into a closely packed lattice1. A variety of two-dimensional systems have shown evidence for Wigner crystals2,3,4,5,6,7,8,9,10,11 (WCs). However, a spontaneously formed classical or quantum WC has never been directly visualized. Neither the identification of the WC symmetry nor direct investigation of its melting has been accomplished. Here we use high-resolution scanning tunnelling microscopy measurements to directly image a magnetic-field-induced electron WC in Bernal-stacked bilayer graphene and examine its structural properties as a function of electron density, magnetic field and temperature. At high fields and the lowest temperature, we observe a triangular lattice electron WC in the lowest Landau level. The WC possesses the expected lattice constant and is robust between filling factor ν ≈ 0.13 and ν ≈ 0.38 except near fillings where it competes with fractional quantum Hall states. Increasing the density or temperature results in the melting of the WC into a liquid phase that is isotropic but has a modulated structure characterized by the Bragg wavevector of the WC. At low magnetic fields, the WC unexpectedly transitions into an anisotropic stripe phase, which has been commonly anticipated to form in higher Landau levels. Analysis of individual lattice sites shows signatures that may be related to the quantum zero-point motion of electrons in the WC lattice. 

Abstract The unusual properties of superconductivity in magic-angle twisted bilayer graphene (MATBG) have sparked considerable research interest^1–13. However, despite the dedication of intensive experimental efforts and the proposal of several possible pairing mechanisms^14–24, the origin of its superconductivity remains elusive. Here, by utilizing angle-resolved photoemission spectroscopy with micrometre spatial resolution, we reveal flat-band replicas in superconducting MATBG, where MATBG is unaligned with its hexagonal boron nitride substrate¹¹. These replicas show uniform energy spacing, approximately 150 ± 15 meV apart, indicative of strong electron–boson coupling. Strikingly, these replicas are absent in non-superconducting twisted bilayer graphene (TBG) systems, either when MATBG is aligned to hexagonal boron nitride or when TBG deviates from the magic angle. Calculations suggest that the formation of these flat-band replicas in superconducting MATBG are attributed to the strong coupling between flat-band electrons and an optical phonon mode at the graphene K point, facilitated by intervalley scattering. These findings, although they do not necessarily put electron–phonon coupling as the main driving force for the superconductivity in MATBG, unravel the electronic structure inherent in superconducting MATBG, thereby providing crucial information for understanding the unusual electronic landscape from which its superconductivity is derived. 

BACKGROUND The past decade has witnessed considerable progress toward the creation of new quantum technologies. Substantial advances in present leading qubit technologies, which are based on superconductors, semiconductors, trapped ions, or neutral atoms, will undoubtedly be made in the years ahead. Beyond these present technologies, there exist blueprints for topological qubits, which leverage fundamentally different physics for improved qubit performance. These qubits exploit the fact that quasiparticles of topological quantum states allow quantum information to be encoded and processed in a nonlocal manner, providing inherent protection against decoherence and potentially overcoming a major challenge of the present generation of qubits. Although still far from being experimentally realized, the potential benefits of this approach are evident. The inherent protection against decoherence implies better scalability, promising a considerable reduction in the number of qubits needed for error correction. Transcending possible technological applications, the underlying physics is rife with exciting concepts and challenges, including topological superconductors, non-abelian anyons such as Majorana zero modes (MZMs), and non-abelian quantum statistics.­­ ADVANCES In a wide-ranging and ongoing effort, numerous potential material platforms are being explored that may realize the required topological quantum states. Non-abelian anyons were first predicted as quasiparticles of topological states known as fractional quantum Hall states, which are formed when electrons move in a plane subject to a strong perpendicular magnetic field. The prediction that hybrid materials that combine topological insulators and conventional superconductors can support localized MZMs, the simplest type of non-abelian anyon, brought entirely new material platforms into view. These include, among others, semiconductor-superconductor hybrids, magnetic adatoms on superconducting substrates, and Fe-based superconductors. One-dimensional systems are playing a particularly prominent role, with blueprints for quantum information applications being most developed for hybrid semiconductor-superconductor systems. There have been numerous attempts to observe non-abelian anyons in the laboratory. Several experimental efforts observed signatures that are consistent with some of the theoretical predictions for MZMs. A few extensively studied platforms were subjected to intense scrutiny and in-depth analyses of alternative interpretations, revealing a more complex reality than anticipated, with multiple possible interpretations of the data. Because advances in our understanding of a physical system often rely on discrepancies between experiment and theory, this has already led to an improved understanding of Majorana signatures; however, our ability to detect and manipulate non-abelian anyons such as MZMs remains in its infancy. Future work can build on improved materials in some of the existing platforms but may also exploit new materials such as van der Waals heterostructures, including twisted layers, which promise many new options for engineering topological phases of matter. OUTLOOK Experimentally establishing the existence of non-abelian anyons constitutes an outstandingly worthwhile goal, not only from the point of view of fundamental physics but also because of their potential applications. Future progress will be accelerated if claims of Majorana discoveries are based on experimental tests that go substantially beyond indicators such as zero-bias peaks that, at best, suggest consistency with a Majorana interpretation. It will be equally important that these discoveries build on an excellent understanding of the underlying material systems. Most likely, further material improvements of existing platforms and the exploration of new material platforms will both be important avenues for progress toward obtaining solid evidence for MZMs. Once that has been achieved, we can hope to explore—and harness—the fascinating physics of non-abelian anyons such as the topologically protected ground state manifold and non-abelian statistics. Proposed topological platforms. (Left) Proposed state of electrons in a high magnetic field (even-denominator fractional quantum Hall states) are predicted to host Majorana quasiparticles. (Right) Hybrid structures of superconductors and other materials have also been proposed to host such quasiparticles and can be tailored to create topological quantum bits based on Majoranas. 

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 (θGr-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. 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.