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Transition of superfluid to insulator is observed in the layer-imbalanced regime of bilayer magnetoexcitons.

A new platform comprising large-scale 2D arrays of quantum dots patterned with sub-nanometre precision, with each quantum dot defined by tens of phosphorus atoms doped into silicon, allows for analogue simulation of quantum materials on arbitrary 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.

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.

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.

The anomalous Hall effect has been observed in high-quality epitaxial thin films of non-collinear antiferromagnet Mn₃Pt, and can be switched on and off using an electric field.

Fractional quantum Hall states in 2D electron gases arise due to strong electron-electron interactions, which makes a general theoretical understanding difficult. Fu et al. present data showing the ν = 5/3 quantum Hall state has a 3/2 plateau in the diagonal resistance that has not been captured by existing models.

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.

It is predicted that fractionally charged skyrmions, topologically protected vortex-like spin configurations, may exist in systems exhibiting fractional quantum Hall states. Here, the authors demonstrate the existence of such objects in GaAs single quantum wells.

A magnetoresistance effect that occurs in a platinum layer deposited on a magnon junction consisting of two insulating magnetic yttrium iron garnet layers separated by an antiferromagnetic nickel oxide spacer layer could be used to create spintronic and magnonic devices that are free from Joule heating.

Electron pairing is a rare phenomenon which can result in exotic behaviour such as superconductivity. Here, the authors evidence robust electron pairing in the quantum Hall edge states of a Fabry–Perot interferometer via Aharonov–Bohm conductance oscillations and quantum shot noise measurements.

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.

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.

This Review describes the concepts behind generalized quantum Hall effects that can take place without a magnetic field, and summarizes recent experimental manifestations of these phenomena in twisted two-dimensional materials and few-layer graphene.

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.

The role of superconducting phase fluctuations in overdoped cuprates remains controversial. Here, the authors observe an unexpected nonmonotonic doping dependence of phase fluctuations in Bi_2+xSr_2−x−yLa_yCuO_6+δ, where vortex-like phase fluctuations are enhanced in both under- and overdoped samples.

Fermionic currents of opposing chirality can be spatially filtered without the need for a magnetic field using the quantum geometry of topological bands in single-crystal PdGa.

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.

Transport measurements of the metallic kagome spin ice HoAgGe show that it has an emergent discrete symmetry that is not apparent from measurements of its magnetization.

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.

Direct measurement of the Berry curvature and the quantum metric of photonic modes in a high-finesse planar microcavity is achieved, enabling quantitative prediction of the independently measured anomalous Hall drift.

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.

The roles of orbitofrontal and cingulate cortex in emotional decisions remain unclear. Here the authors show distinct timing between caudal orbitofrontal and cingulate signals, that orbitofrontal stimulation increases avoidance, and that physiological responses mirror behavior.

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.

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.

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.

Hall resistance quantization measurements in the quantum anomalous Hall effect regime on a device based on the magnetic topological insulator V-doped (Bi,Sb)₂Te₃ show that the system can provide a zero external magnetic field quantum standard of resistance.

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

A combined experimental and theoretical approach identifies the van der Waals material Fe₃GeTe₂ as a candidate ferromagnetic nodal line semimetal. These results extend the connections between topology and magnetism.

Valley dependent spin polarization called spin-valley locking appears in absence of magnetism but it is limited to rare examples of transition metal dichalcogenides. Here, the authors report evidence of spin-valley locking and stacked quantum Hall effect in a bulk Dirac semimetal BaMnSb₂.

Previous studies of skyrmions in thin film architectures have shown widely-varying magnitudes of the topological Hall effect. Here, Raju et al. show that this variation follows a power-law behaviour driven by chiral spin fluctuations at the phase transition between isolated and lattice skyrmions.

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 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.

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.

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 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.

Solidification upon heating, known as Pomeranchuk effect, is a known phenomenon for 3He. Here, leveraging on the hybridization of organic molecules orbitals with those of inorganic elements in polymers, the authors report the Pomeranchuk effect within an electronic system and the impact of magnetic fields on it.

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.

Material with both topological state and magnetic order remains rare. Here, Ueda et al. observe a sizable spontaneous Hall conductivity with minimal magnetization at a few Kelvin below the all-in-all-out magnetic ordering temperature in the predicted magnetic Weyl semimetal R₂Ir₂O₇.

A metallic p-wave magnet with commensurate spin helix and anisotropic electronic properties is experimentally realized and shows a giant anomalous Hall effect when distorted by a tiny spontaneous magnetization.

Quantum Hall liquids play host to a wide range of unusual physics. Here, the authors use an electronic Fabry-Pérot interferometer to observe modulations of a quantum Hall liquid’s area, which can offer a means to study the statistics of fractional charges.

Observation of quantum phenomena in correlated electron systems is challenging due to low mobility and high concentration of carriers. Here, Matsubara et al. report a two-dimensional electron system with high mobility-low carrier density in δ-doped SrTiO₃, demonstrating quantum Hall effect in d-electron systems.

The evolution of the quantum Hall state from bulk spectrum to edge state remains obscure. Here, Patlatiuk and Scheller et al. observe magnetic compression against a hard edge followed by motion into the bulk and depopulation of the integer quantum Hall edge states, in agreement with the bulk-to-edge correspondence.

Two dimensional electron gas (2DEG) at oxide interfaces is promising in modern electronic devices. Here, Wadehra et al. realize 2DEG at a novel interface composed of LaVO₃ and KTaO₃, where strong spin-orbit coupling and relativistic nature of the electrons in the 2DEG, leading to anisotropic magnetoresistance and planar Hall effect.

Conventional type 1 dendritic cells (cDC1) can boost the precursor exhausted T cell population thought to be essential for efficacy of immune checkpoint therapy. Here the authors enhance this cellular network using Flt3L to expand cDC1s and then map the movement of T cells and DCs between tumors and lymph nodes.

Magnetic skyrmions are promising objects for future spintronic devices. However, a better understanding of their dynamics is required. Here, the authors show that in contrast to predictions the skyrmion Hall angle is independent of their diameter and motion is dominated by disorder and skyrmion-skyrmion interactions in the system.

In general, heating increases disorder and leads to the loss of magnetism in condensed matter. Here, the authors demonstrate that a normal metal can be magnetized by applying a temperature gradient during non-uniform heating when attached to a magnetic insulator.