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Bilayer graphene has been shown to host fractional quantum Hall states. Here, the authors observe the fractional quantum Hall states at quarter- and half-filled Landau levels and the alternation of anti-Pfaffian and Pfaffian phases at half fillings.

Graphene was one of the first materials proposed to host the quantum spin Hall effect. However, its weak intrinsic spin-orbit interaction means that observing such an effect requires modifying the graphene band structure. Here, Ghiasi et al. combine graphene with CrPS₄ and detect quantum spin Hall states at zero magnetic field.

Magnetically intercalated transition metal dichalcogenides provide a platform to study the interplay of magnetism, electronic band structures, and correlations. Here the authors demonstrate a nearly magnetization-free anomalous Hall effect, collinear antiferromagnetism and non-Fermi liquid behavior in V_1/3NbS₂.

The current known two-dimensional topological insulators with small band gaps limit the potential for room temperature applications. Here, Chen et al. observe a sizable gap of 129 meV in a 1T'-WSe₂ single layer grown on bilayer graphene with in-gap edge state near the layer boundary.

The spin Hall effect and its inverse allow conversion between charge and spin currents in both magnetic and nonmagnetic materials. Weiet al.observe an anomaly in the temperature dependence of the inverse spin Hall effect, which suggests that it can also be used as a sensor for very small magnetic moments.

The transport properties of materials with topologically non-trivial band structures may be manipulated by an applied magnetic field or by magnetic doping. Here, the authors demonstrate quantum Hall states for temperatures up to 2 K in thin film bilayers comprising pristine and Cr-doped topological insulators.

Quantized magnetoelectric coupling, which induces exotic magneto-optical phenomena, awaits to be evidenced in topological insulators. Here, Okada et al. demonstrate Faraday and Kerr rotations of magnetic topological insulator surfaces in quantum anomalous Hall states by terahertz magneto-optics, indicating topological magnetoelectric effect.

Three-dimensional topological insulators are materials that are nonmagnetic insulators in the bulk but exhibit metallic surface states. Yoshimi et al, now identify a signature of such two-dimensional states, the quantum Hall effect, in bismuth-based chalcogenide topological insulators.

Andreev reflection is normally known to occur at a metal-superconductor interface. Here, Hashisaka et al. observe an Andreev-like process in a narrow junction between fractional and integer quantum Hall states originating from a topological quantum many-body effect instead of superconductivity.

A graphenep–njunction can be created by connecting electrical gates that generate electron-doped and hole-doped areas in a flake. Here, the authors use shot-noise measurements to provide microscopic evidence that edge states are uniquely mixed along the junction in the quantum Hall regime.

Skyrmions, when driven by any applied force, experience an addition sideways motion known as the skyrmion hall effect. Here, Brearton et al. present a reciprocal space method for determining the strength of the skyrmion hall effect, making measurement possible for skyrmion lattices.

A superconductor–graphene junction is shown to exhibit the quantum Hall effect, with the chemical potential of the edge state displaying a sign reversal. Such a system could provide a platform for observing isolated non-Abelian anyonic zero modes.

Spin–orbit torques could enable a new generation of low-power electrically controlled memory devices. Here, the authors experimentally disentangle the spin-Hall effect and inverse spin-galvanic effect contributions to the relativistic spin torques in a room temperature Fe/(Ga,Mn)As bilayer.

The authors report a Hall effect that originates from a fictitious magnetic field associated with antiferromagnetic order that breaks time-reversal symmetry, followed by translation symmetry.

In organic semiconductors, disorder-induced traps can alter the mobility of the charges and introduce noise in transport measurements. It is now shown that simple drop-casting of perfluoropolyether on top of organic single-crystals is an effective strategy for healing charge traps. This method allows the intrinsic transport properties of these materials to be recovered as well as suppressing noise in Hall effect measurements.

Graphene on boron nitride gives rise to a moiré superlattice displaying the Hofstadter butterfly: a fractal dependence of energy bands on external magnetic fields. Now, by means of capacitance spectroscopy, further aspects of this system are revealed—most notably, suppression of quantum Hall antiferromagnetism at particular commensurate magnetic fluxes.

Future information storage technology may exploit electrical currents to write the states of ferromagnetic nanoelements via spin torque effects. Here, the authors demonstrate such behaviour promoted by exchange bias from an interfaced antiferromagnet, which may help overcome practical device limitations.

Charge-neutral graphene in the quantum Hall regime is known to be an insulator. Now thermal transport measurements show that it also does not conduct heat. This sheds light on the nature of the ground state in this regime.

Energy relaxation crucially impacts transport properties of mesoscopic devices. Here the authors show that energy can be distributed between distant parts of the sample, which may provide a resolution to an outstanding puzzle concerning energy conservation in transport through quantum Hall edges.

The fractional quantum Hall effect, occurring for rational Landau-level filling factors, is commonly observed in GaAs heterostructures. Now, unusual even-denominator fractional quantum Hall states are reported for an oxide 2D electron system.

The effect of disorder in conventional two-dimensional electron systems is usually described in terms of individual electrons interacting with an underlying disorder potential. Scanning single-electron transistor measurements of graphene in a strong magnetic field indicate that in this system, coulombic interactions between electrons must also be taken into account.

The ground state of charge-neutral bilayer graphene in a strong magnetic field is not fully determined. Now thermal transport measurements show an absence of heat flow through that state, suggesting that its collective excitations could be gapped.

A technique that allows the electrical detection of spin-polarized transport in semiconductors without disturbing the spin-polarized current or using magnetic elements has now been demonstrated. The approach could lead to the integration of spintronics elements into semiconductor microelectronic circuits.

Kwak et al. report AC magnetic parallel dipole line Hall measurements on electrochemical random-access memory based on WO_3-x, which determine the oxygen donor level and reveal that conductance potentiation even at low temperature is caused by an increase in both mobility and carrier density.

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.

Quantum Hall ferromagnets can host magnons, collective spin-wave excitations, which have possible uses in spin-wave based information processing. Detecting these excitations electrically can be challenging. Here, Kumar, Srivastav, Roy, Park and coauthors demonstrate a noise-based approach to detecting magnons.

The classification of magnets now includes altermagnets which possess opposite-spin sublattices connected by rotation and share some features with ferro- and antiferromagnets. Here the authors report the anomalous Hall effect in Mn5Si3 and interpret the results in terms of a d-wave altermagnetic phase.

We show that domain walls in minimally twisted bilayer graphene support exceptionally robust proximity superconductivity in the quantum Hall regime.

The Hall effect has been used as a probe of the normal state of cuprates, when superconductivity is supressed by a magnetic field. Here, the authors report the vanishing of the Hall coefficient at high magnetic field in cuprates with stripe order and interpret it as a signature of the stripe-ordered phase.

The knowledge of quantum numbers of the edge modes is essential for understanding fractional Hall states containing counter-propagating downstream and upstream modes. Here the authors identify the edge quantum numbers by probing a crossover from non-equilibrated to equilibrated edge mode regime in thermal conductance.

The quantum Hall effect in GaAs-based devices defines resistance standards accurate to within one part in 10⁻⁹ at magnetic fields close to 10 T. Here, Lafont et al. demonstrate such accuracies over an extended magnetic field range at 1.4 K in chemically vapour-deposited graphene on silicon carbide.

Measuring real time magnetization dynamics resulting from Hall effects is hard due to the small signal size. Here Sala et al demonstrate a method of performing Hall resistance measurements with sub-ns resolution, and use it to investigate the switching of GdFeCo dots induced by spin-orbit torques.

Control of magnetization is important for applications in spintronics. Now, the piezomagnetic effect allows strain to control the anomalous Hall effect in a metal at room temperature by rotating its antiferromagnetic order.

Hybrid perovskites exhibit long carrier diffusion lengths and lifetimes. Here, Chen et al. show experimentally that carrier recombination in perovskites is far from Langevin and closer to the best direct-bandgap semiconductors, which can be explained by the dipolar polaronic nature of charge carriers.

Theories predict a large thermopower and a quantized thermoelectric Hall conductivity in topological semimetals. Here, the authors observe an ultrahigh longitudinal thermopower and a giant power factor attributed to the quantized thermoelectric Hall effect in a Weyl semimetal TaP.

The manipulation of domain walls in magnetic materials is attracting interest because of its potential use in memory devices. Chibaet al. demonstrate that the velocity of domain walls in perpendicularly magnetized films can be changed by more than an order of magnitude by applying an electric field.

The nature of the fractional quantum Hall state when the lowest Landau level is half-filled remains controversial. Now, the observation of a topological phase transition at related filling fractions suggests that the half-filled state is non-Abelian.

The kagome magnet Co₃Sn₂S₂ has complex magnetic behaviour and a topological band structure that yields a large anomalous Hall effect. Guguchia et al. find phase separation between ferro- and anti-ferromagnetic orders and that the volume-wise competition controls the anomalous Hall conductivity

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.

Magnetoresitance (MR) is a tool to study electronic transport and spin order in metals. Here, the authors demonstrate two different microscopic origins of antisymmetric linear MR from both Zeeman-split Fermi surface and anomalous electron velocity.

Recently graphene has emerged as a new platform for the study of quantum Hall states. Here, by means of noise measurements, the authors report evidence for the existence of the upstream mode and its ballistic nature in the hole-conjugate fractional quantum Hall state in a bilayer graphene device.

The spontaneous topological Hall effect, combining non-coplanar antiferromagnetic order with finite scalar spin chirality in the absence of a magnetic field, is now experimentally demonstrated for the triangular lattice compounds CoTa₃S₆ and CoNb₃S₆.

The broken-symmetry edge states that are the hallmark of the quantum Hall effect in graphene have eluded spatial measurements. Here, the authors spatially map the quantum Hall broken-symmetry edge states using atomic force microscopy and show a gapped ground state proceeding from the bulk through to the quantum Hall edge boundary.

It was suggested that the breakdown of the quantum Hall effect in graphene originates from the coupling between counter propagating edge modes. Here, by using scanning gate microscopy, the authors propose a microscopic mechanism of this coupling due to antidots present at graphene edges.

Exploring photon-polariton interactions advances not only the understanding of polariton dynamics but also the modern technologies. Here the authors take advantage of strong coupled magnons and microwave photons in a cross-cavity to achieve tunable cavity magnon polariton transport which can be potentially applied as logic devices.

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.