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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.

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.

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

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.

The authors reveal that the ferroelectric to antiferroelectric phase transition in Pb(Zr_0.97Ti_0.03)O₃-1wt%Nb₂O₅ at low temperatures is an irreversible process exhibiting relaxation behavior and diffusional kinetics.

Exotic six- and eight-particle excitonic complexes have recently been observed in 2D semiconductors. Here, the authors uncover a stable many-body exciton in WSe₂–comprising 20 interacting quasiparticles–that emerges when strong electrostatic doping fills the Q valley.

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.

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.

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.

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.

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.

Magnetoresistance is a fundamental transport phenomenon that provides deep insight into electronic structure, magnetic order and emergent quantum effects in solids. This Primer reviews major magnetoresistance phenomena and presents practical measurement methodologies, emphasizing experimental configurations, instrumental limitations, common artefacts and best practices for reliable data interpretation.

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.

In this work, researchers build a scalable photonic Chern insulator by twisting a fibre during fabrication, breaking an effective time-reversal symmetry and inducing a pseudo-magnetic field. The team reveals a ‘Goldilocks’ regime that guarantees topological protection against fabrication-induced disorder of any symmetry class in the fibre cross-section.

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.

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.

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.

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.

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.

The authors study microstructured UTe₂ by high-field transport, focusing on the field-reinforced superconducting phase. They reveal a highly-directional vortex pinning force typical of quasi-2D superconductors, indicating a vortex lock-in state and consistent with a change of order parameter from the low-field superconducting phase.

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.

Scanning tunnelling microscopy is used to image pristine electrostatically defined quantum Hall edge states in graphene with high spatial resolution and demonstrate their interaction-driven restructuring.

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.

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.

When 100 social and behavioural science claims were examined, 34% of reanalyses closely matched the original results, with 74% reaching the same conclusion, revealing limited robustness of single-path analyses and the need to address analytical uncertainty.

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.

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.

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.

Layered van der Waals magnets like CrSBr, when sandwiched between electrodes form a natural magnetic tunnel junction, albeit lacking the characteristic nonmultiple volatile states at zero field of a magnetic memory. Here, Chen et al overcome this limitation to establish four nonvolatile states at zero field by constructing magnetic tunnel junctions out of twisted monolayers and bilayers of CrSBr with two twisted interfaces.

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.

A 3D quantum Hall effect has been reported in Dirac semimetal ZrTe₅ due to a magnetic-field-driven Fermi surface instability. Here, the authors show evidence of quasi-quantized Hall response without Fermi surface instability, but they argue that it is due to the interplay of the intrinsic properties of ZrTe₅ electronic structure and Dirac semi-metallic character.

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.