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A picture of how heavy fermions acquire their mass enhancement has now been obtained using scanning tunnelling spectroscopy.

Topological surface states are a class of electronic states that might be of interest in quantum computing or spintronic applications. They are predicted to be robust against imperfections, but so far there has been no evidence that these states do transmit through naturally occurring surface defects. Here, scanning tunnelling microscopy has been used to show that topological surface states of antimony can be transmitted through naturally occurring barriers that block non-topological surface states of common metals.

Strong electron–electron interactions in magic-angle twisted bilayer graphene can fundamentally change the topology of the system’s flat bands, producing a hierarchy of strongly correlated topological insulators in modest magnetic fields.

Majorana fermions, particles which are their own antiparticles, are predicted to exist in systems combining superconductivity and topologically non-trivial band structure. Here, the authors propose means to create and manipulate such excitations in one-dimensional chains of adatoms on superconducting surfaces.

Local probes of quantum Hall states are still in their infancy. Now scanning tunnelling measurements were used to extract the energy gap of candidate non-Abelian fractional states, which are found to be encouragingly large for applications.

High-resolution scanning tunnelling microscopy measurements show that chains of magnetic atoms on the surface of a superconductor provide a promising platform for realizing and manipulating Majorana fermion quasiparticles.

The conducting surface states of 3D topological insulators are two-dimensional. In an analogous way, the edge states of 2D topological insulators are one-dimensional. Direct evidence of this one-dimensionality is now presented, by means of scanning tunnelling spectroscopy, for bismuth bilayers—one of the first theoretically predicted 2D topological insulators.

Moiré systems formed by 2D atomic layers have widely tunable electrical and optical properties and host exotic, strongly correlated and topological phenomena, including superconductivity, correlated insulator states and orbital magnetism. In this Viewpoint, researchers studying different aspects of moiré materials discuss the most exciting directions in this rapidly expanding field.

High-resolution STM/STS visualizes the fractionalization of flat moiré bands into discrete Hofstadter subbands in moiré graphene near the predicted second magic angle, and experimentally establishes several fundamental properties of the fractal Hofstadter energy spectrum.

Insulating states that are formed because of pairing between electrons and holes are known to exist in engineered bilayer structures in high magnetic fields. Now evidence suggests they can occur in a monolayer crystal at zero field.

A magnetic-field-induced Wigner crystal in Bernal-stacked bilayer graphene was directly imaged using high-resolution scanning tunnelling microscopy and its structural properties as a function of electron density, magnetic field and temperature were examined.

A long-standing question has been the interplay between pseudogap, which is generic to all hole doped copper oxide superconductors, and stripes, whose static form occurs in only one family of copper oxides over a narrow range of the phase diagram. This study reports observations of the spatial reorganization of electronic states with the onset of the pseudogap state at T^* in the high temperature superconductor Bi₂Sr₂CaCu₂O_8+x using scanning tunnelling microscopy. The onset of the pseudogap phase coincides with the appearance of electronic patterns that have the predicted characteristics of fluctuating stripes. The experiments indicate that stripes are a consequence of pseudogap behaviour rather than its cause.

Angle-resolved photoemission spectroscopy of superconducting magic-angle twisted bilayer graphene reveals flat-band replicas that are indicative of strong electron–phonon coupling; these replicas are absent in non-superconducting twisted bilayer graphene.

Twisted double bilayer graphene hosts flat bands that can be tuned with an electric field. Here, by using gate-tuned scanning tunneling spectroscopy, the authors demonstrate the tunability of the flat band and reveal spectral signatures of correlated electron states and the topological nature of the flat band.

A scanning tunnelling microscopy technique that minimally perturbs the sample quantifies the interacting phase diagram of the zeroth Landau level in monolayer graphene.

High-resolution scanning tunnelling microscopy is used to observe the quantum textures of the many-body wavefunctions of the correlated insulating, pseudogap and superconducting phases in magic-angle graphene.

A study combining tunnelling and Andreev reflection spectroscopy with a scanning tunnelling microscope provides evidence for unconventional superconductivity in magic-angle twisted bilayer graphene.

The electronic properties along the out-of-plane direction of layered materials are often inferred indirectly. Here, Gyenis et al. directly probe in cross-section the quasi-two-dimensional correlated electronic states of the heavy fermion superconductor CeCoIn₅.

Electron–electron interactions in magic-angle twisted bilayer graphene can split usually degenerate electronic bands, giving rise to a cascade of electronic transitions revealed by spectroscopy.

A phase of strongly interacting electrons that has a spontaneous dipole moment is seen for the first time using an approach that images the electron's wavefunction through interference at an impurity.

By means of low-temperature scanning tunnelling spectroscopy, a heavy fermion material in its superconducting and mixed states can be imaged. Besides probing the superconducting gap symmetry, the measurements also reveal a pseudogap.

Three-dimensional Dirac semimetals such as Cd₃As₂ are attracting attention because their electronic structure can be considered to be the three-dimensional analogue of graphene’s. Low-temperature scanning tunnelling measurements of the 112 cleavage plane of Cd₃As₂ now reveal its electronic structure down to atomic length scales, as well as its Landau spectrum and quasiparticle interference pattern.

Topological insulators are materials in which a relativistic effect known as spin–orbit coupling gives rise to surface states that resemble chiral edge modes in quantum Hall systems, but with unconventional spin textures. It has been suggested that a feature of such spin-textured boundary states is their insensitivity to spin-independent scattering, which is thought to protect them from backscattering. Here, scanning tunnelling spectroscopy and angle-resolved photoemission spectroscopy are used to confirm this prediction.

Helical Dirac fermion states in topological insulators could enable dissipation-free spintronics and robust quantum information processors. A study of the influence of disorder on these states shows that although they are resilient against backscattering by magnetic impurities, fluctuations caused by charge impurities could cause problems for such applications.

The first spatially resolved measurements of gap formation in a high-T_c superconductor are reported. Over a wide range of doping (0.16 to 0.22), it is found that pairing gaps nucleate in nanoscale regions above T_c. These regions proliferate as the temperature is lowered, resulting in a spatial distribution of gap sizes in the superconducting state.

Majorana zero modes — useful for quantum computing — are revealed in carbon nanotubes by utilizing a synthetic spin–orbit interaction.

An ideal topological insulator possesses an insulating bulk and a unique conducting surface however such behaviour is typically inhibited by bulk conduction due to defects. Here, the authors show that Sn-doped Bi_1.1Sb_0.9Te₂S grown by the vertical Bridgman technique might overcome this hurdle.

A catalogue of the naturally occurring three-dimensional stoichiometric materials with flat bands around the Fermi level provides a powerful search engine for future theoretical and experimental studies.

The study of the band structure and crystal symmetry of the semimetal bismuth indicates that this material is a higher-order topological insulator hosting robust one-dimensional metallic states on the hinges of the crystal.

Chiea Chuen Khor, Tin Aung, Francesca Pasutto, Janey Wiggs and colleagues report a global genome-wide association study of exfoliation syndrome and a fine-mapping analysis of a previously identified disease-associated locus, LOXL1. They identify a rare protective variant in LOXL1 exclusive to the Japanese population and five new common variant susceptibility loci.

When it comes to superconducting device components, there is no such thing as too thin, but superconductivity has its limits. Now, ultrathin lead films with crystalline perfection have been shown to be able to carry large dissipationless currents down to a thickness of a few monolayers.

Apicco and colleagues show that reducing TIA1 inhibits tau-mediated neurodegeneration and improves survival in a mouse model of tauopathy. This rescue occurs with a transition in tau aggregation from oligomeric to fibrillar forms of tau. These findings suggest a key role for RNA binding proteins in the pathophysiology of tau.

Scanning tunnelling microscopy shows that 1D channels between quantum Hall states with different valley polarization are metallic or insulating depending on constraints imposed on electron–electron interaction by valley flavour.

Scanning tunnelling spectroscopy and extended-Hubbard-model cluster calculations reveal that magic-angle twisted bilayer graphene is a strongly correlated electron system, similar to other unconventional superconductors.

Moiré materials are an emerging class of strongly correlated quantum materials designed by the rotational or lattice misalignment of 2D crystals. This Review discusses how local probe techniques are uniquely positioned to elucidate the microscopic mechanisms underlying the electronic phases in moiré materials.

Physicists have managed to watch individual hydrogen atoms move on metal surfaces at very low temperatures — in defiance of classical physics.

Three-dimensional analogues of graphene have recently been synthesized. The transport properties of such a Dirac semimetal, Cd₃As₂, have been studied, revealing an unexpected mechanism that suppresses backscattering dramatically.