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Magneto-oscillations have revealed many interesting phenomena in graphene and quantum Hall systems, but they are typically measured at low currents and in equilibrium. Here, the authors report several non-equilibrium quantum effects observed in magneto-oscillations in graphene at high currents.

Landau states are associated with the quantised orbits of charged particles in magnetic fields. By manipulating electron vortex beams in a magnetic field, this study reconstructs the internal quantum dynamics of free-electron Landau states, which differs strongly from the classical cyclotron rotation.

SQUID-on-tip tomographic imaging of Landau levels in magic-angle graphene provides nanoscale maps of local twist-angle disorder and shows that its properties are fundamentally different from common types of disorder.

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

Stimulated Raman scattering is one of the methods being explored to generate ultrahigh intensity short laser pulses. Depierreux et al. explore a new regime, also relevant to inertial confinement thermonuclear fusion, in which nonlinear kinetic response of a hot plasma enhances Raman amplification.

Monitoring the photocurrent generated as a laser scans across a graphene field-effect device subjected to low temperature and high magnetic fields enables the spatial distribution of Landau levels across a graphene sheet to be mapped. This in turn allows the relative contribution of bulk and edge states to the macroscopic electrical characteristics of these devices to be determined.

Various fractional quantum Hall phases are observed in a new generation of bilayer-graphene-based van der Waals heterostructures, including an even-denominator state predicted to harbour non-Abelian anyons.

While the electronic quality of graphene has significantly improved during the last two decades, charged defects inside encapsulating crystals still limit its performance. Here, the authors overcome this limitation and report the enhanced electronic quality of graphene enabled by tuneable Coulomb screening inside large-angle twisted bilayer and trilayer graphene devices, showing Landau quantization at magnetic fields down to ~5 mT.

The dynamics of hole-conjugated fractional quantum Hall states is poorly understood due to the limitations of current experimental probes. Here the authors study the high-frequency dynamics of edge modes at filling factor 2/3, precisely identifying the tunneling charge and damping of constituent charge modes.

In some iron-based materials, unconventional superconductivity can emerge near a quantum phase transition where long-range magnetic order vanishes. Giovannettiet al.show that the magnetic quantum phase transition in an iron pnictide superconductor is very close to the quantum tricritical point.

A hybrid topological phase of matter is discovered in the simple elemental-solid arsenic and explored using tunnelling microscopy, photoemission spectroscopy and a theoretical analysis.

Electronic systems with inverted band structures can support exotic topological insulator and exciton condensate states. Here, the authors demonstrate the formation of a helical exciton condensate in quantum Hall bilayers, and a quark-like quasiparticle confinement-deconfinement transition.

Chorus waves are crucial on radiation belt dynamics in the space of magnetized planets. Here, the authors show that initially excited single-band chorus waves can quickly accelerate medium energy electrons, and divide the anisotropic electrons into low and high energy components, which subsequently excite two-band chorus waves.

Most of the notable properties of graphene are a result of the cone-like nature of the points in its electronic structure where its conduction and valance bands meet. Similar structures arise in 2D HgTe quantum wells, but without the spin- and valley-degeneracy of graphene; their properties are also likely to be easier to control.

Graphene and topological-insulator surfaces are well known for their two-dimensional conic electronic dispersion relation. Now three-dimensional hyperconic dispersion is shown for electrons in a HgCdTe crystal—once again bridging solid-state physics and quantum electrodynamics.

The recently-developed topological heavy fermion model explains the low energy electrons of magic-angle twisted bilayer graphene as a hybridization between states localized at AA stacking sites and itinerant topological states, denoted by f and c electrons in analogy to heavy fermion systems. Here, the authors extend this model to a nonzero magnetic field, obtaining interacting Hofstadter spectra in the flatband limit by analytic methods.

Polar skyrmions are nanoscale topological structures of electric polarizations. Their collective modes, dubbed as “skyrons”, are discovered by the terahertz-field-excitation, femtosecond x-ray diffraction measurements and advanced modeling.

Two-dimensional massive and massless Dirac fermions in HgTe/CdHgTe quantum wells yield terahertz Landau emission. The emission frequency is continuously tunable with magnetic field or carrier concentration, over the range from 0.5 to 3 THz.

Scanning tunnelling microscopy is used to reveal a new topological kagome magnet with an intrinsic Chern quantum phase, which shows a distinct Landau fan structure with a large Chern gap.

Understanding collective behaviour is an important aspect of managing the pandemic response. Here the authors show in a large global study that participants that reported identifying more strongly with their nation reported greater engagement in public health behaviours and support for public health policies in the context of the pandemic.

The technological application of ultrafast terahertz magnons in itinerant ferromagnetic nanostructures is currently limited by magnon relaxation due to Landau damping. Here, Qin et al. demonstrate suppressed Landau damping and enhanced magnon lifetimes in ultrathin films of Fe–Pd alloy.

Increasing the size of mesoscopic devices based on van der Waals heterostructures triggers additional quantum effects. Here, the authors observe distinct magnetoresistance oscillations in graphene/h-BN Hall bars only in devices wider than 10 μm due to resonant scattering of charge carriers by transverse acoustic phonons in graphene.

Transistors that operate by the passage of electrons through a single-dopant atom achieve the ultimate limit for the miniaturization of electronic devices, but only when multiple transistors are intimately connected can they become useful. Roche et al. demonstrate the equivalent of just this, connecting two such transistors to build a two-atom electron pump.

A nitrogen impurity in diamond—where two of the carbon atoms are replaced by a nitrogen atom and a vacant lattice site—is seen as a valuable qubit. The spin of an electron localized to the nitrogen-vacancy centre is commonly used for processing. Researchers now show that this electron spin state can be transferred to the nitrogen nuclear spin, where it can be stored until needed.

In Weyl semimetals, unusual electronic transport phenomena are predicted to occur, such as an axial anomaly which violates the conservation of chiral fermions. Here, the authors evidence such behaviour via the occurrence of negative magnetoresistance in layered high-purity non-magnetic metals.

Owing to electron localization, two-dimensional materials are not expected to be metallic at low temperatures, but a field-induced quantum metal phase emerges in NbSe₂, whose behaviour is consistent with the Bose-metal model.

Recent work has reported a realization of a time crystal in the form of the Bose-Einstein condensate of magnons in superfluid ³He. Here, the authors study the dynamics of a pair of such quantum time crystals and show that it closely resembles the evolution of a two-level system, modified by nonlinear feedback.

Most space plasmas are in turbulent state and turbulence plays an essential role in transferring energy from large to small scales. Here, the authors show direct measurements of ion cyclotron damping in the Earth’s turbulent magnetosheath plasma and the resulting ion and electron energization rates.

There is a long-standing experimental effort to observe field-induced correlated states in three-dimensional materials. Here, the authors observe an unconventional Hall response in the quantum limit of the bulk semimetal HfTe₅ with a plateau-like feature in the Hall conductivity.

UTe₂ is a proposed intrinsic topological superconductor, but its quasiparticle surface band has not yet been visualized. Now this is achieved using quasiparticle interference imaging, revealing the symmetry of the superconducting order parameter.

The authors find the electric-field-driven motion of domain walls in the improper ferroelectric ErMnO₃, showing that they readily return to their initial position after having travelled distances exceeding 250 nm.

Finite momentum superconducting pairing refers to a class of unconventional superconducting states where Cooper pairs acquire a non-zero momentum. Here the authors report a new superconducting state in bulk 4Hb-TaS₂, where magnetic fields induce finite momentum pairing via magnetoelectric coupling.

Moiré superlattices arising in bilayer graphene coupled to hexagonal boron nitride provide a periodic potential modulation on a length scale ideally suited to studying the fractal features of the Hofstadter energy spectrum in large magnetic fields.

Machine learning tools allow to extract dynamical systems from data, however this problem remains challenging for networks and systems of interacting agents. The authors introduce an approach to learn a predictive model for the dynamics of coupled agents in the form of partial differential equations using emergent spatial embeddings.

Artificial gauge fields unlock additional degrees of freedom to manipulating light in structured photonic systems. This Review strives to unify topological, non-Abelian and non-Hermitian photonics using the concept of gauge fields.

Pump-probe techniques—where a system is driven into a nonequilibrium state and then studied as a function of time—provide rich information about the behaviour of charge carriers and their interactions. Here, Yoo et al extend this class of techniques by injecting electrons at a selected energy and observing their decay in energy and momentum space.

The interplay between electronic topology and superconductivity is of great current interest in condensed matter physics. Here, the authors unveil an unconventional two-dimensional superconducting state accompanied by a van Hove singularity in the recently discovered Dirac nodal line semimetal ZrAs₂, which is exclusively confined to the top and bottom surfaces.

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 study using scanning tunnelling microscopy reveals a charge-density-wave state that is sensitive to magnetic fields and strongly intertwined with superconductivity in the heavy-fermion triplet superconductor UTe₂.