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The properties of edge states at the boundary between a quantum Hall insulator and a superconductor have recently been under scrutiny. Here, the authors find theoretically that Andreev reflection of an edge state is possible only if the superconductor is in the disordered limit, leading to stochastic edge state conductance and providing an explanation of a recent experiment.

Excitonic pairing in fractional quantum Hall states shows two new quantum phases, including a fractional exciton condensate and an unusual type of exciton that obeys fermionic or anyonic quantum statistics.

Previous measurements of interferometers based on quantum Hall (QH) edge channels have suggested potential electron pairing effects. Here, the authors investigate the coupling between QH edge channels in graphene Aharonov-Bohm (AB) interferometers, proposing a possible single-particle explanation for the apparent interference phase jumps and AB frequency doubling.

Topological states in atomically thin quantum spin Hall insulators suffer from instability against environmental factors. Here, the authors devise a strategy to preserve topologically protected states in monolayer indenene through graphene intercalation.

Recently, anyonic statistics were observed in collision experiments on fractional quantum Hall states. Here the authors report signatures of anyonic statistics in the integer quantum Hall state with two copropagating channels, where electrons are split into fractional charges by inter-channel interaction.

The anomalous Hall effect (AHE) occurs in ferromagnets caused by intrinsic and extrinsic mechanisms. Here, Yoo et al. report large anomalous Hall conductivity and Hall angle at the interface between a ferromagnet La_0.7Sr_0.3MnO₃ and a semimetallic SrIrO₃, due to the interplay between correlated physics and topological phenomena.

Guided by density functional theory, a commercially viable refractory alloy is developed, which exhibits excellent room-temperature ductility and strength, and high strength at elevated temperatures.

Polariton condensation of topological propagating edge states is demonstrated with halide perovskite microcavities.

Using ultracold atoms trapped in an optical lattice, a Laughlin-like fractional quantum Hall state is prepared and mapped out on a microscopic level.

New functionalities of two-dimensional topological insulators (2DTI) are of current scientific interest. Here, the authors show that topological protection can be lifted by pairwise coupling of 2DTI bismuthene edges in close proximity.

Polycrystalline thin films of elemental bismuth exhibit a room-temperature nonlinear transverse voltage due to geometric effects of surface electrons that is tunable and can be extended to efficient high-harmonic generation at terahertz frequencies.

In most materials, the hall conductivity has a scaling to the longitudinal resistance that varies between linear and quadratic. Here, Zhang et al demonstrate a hall conductivity proportional to the fifth power of the longitudinal conductivity in Mn₃Si₂Te₆, which they attribute to enhanced force on charge carriers due to chiral orbital currents.

By combining satellite observations with ground-based data and expert validation, this analysis demonstrates considerable misestimation of grassland extent and thereby carbon stock estimates in previous global assessments based on remote sensing.

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.

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 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 topological nature of the electronic structure of two-dimensional ferromagnetic SrRuO₃ and its relationship to the anomalous Hall effect is explored through transport measurements, angle-resolved photoemission spectroscopy and theoretical modelling.

Ultracold atoms in optical lattices exhibit many exotic phenomena. Using interacting spinor Bose gases as a model, Li et al.show how spin-valley degeneracy arising in a multivalley band is broken by quantum fluctuations, resulting in a counterintuitive chiral spin order and a spontaneous spin Hall effect.

Excitations of the fractional quantum Hall states are of great interest because they obey anyonic statistics, but electronic interferometers give contrasting results about their quantum coherence. Here the authors use novel two-particle time-domain interferometry to show that quantum coherence is indeed preserved.

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.

Skyrmion crystals, where skyrmions are arranged close packed in a triangular lattice arise due to the superposition of three magnetic spin spirals, each with a distinct wave vector, Q. Such skrymion crystals have been found in a diverse array of materials. Here, Park et al find a short wavelength (or dense skyrmion) limit of this skyrmion crystal structure in Co1/3TaS2, a metallic triangular lattice antiferromagnet, in the form of a triple Q magnetic ordering, with four magnetic sublattices.’

Kondo systems offer a rich platform to study the interplay between strong correlations and topology. Here the authors observe a large anomalous Hall conductivity in a Kondo ferromagnet USbTe, which they attribute to the Berry curvature originating from flat bands induced by the Kondo hybridization.

Mechanisms for generating spin-polarized currents may be helpful for applications. Now one such mechanism that uses the unusual Landau-level spectrum of WSe₂ under a strong magnetic field is demonstrated.

The transport behaviour of counter-propagating edge modes in the hole-conjugate fractional quantum Hall state is not fully understood. Here, by combining local noise thermometry and thermal conductance measurements, the authors show the absence of thermal equilibration on the edge at macroscopic distances.

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 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.

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.

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 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.

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.

Spin-hall nano-oscillators have potential for use in neuromorphic computing applications. Normally they are based around combination platinum and permalloy. Here, the authors combine a permalloy ferromagnet with a low magnetic damping ferrimagnet, leading to significantly improved performance.

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.

High-mobility graphene can play host to exciton polaritons—hybrid matter–light particles, which can form into a state known as a quantum Hall polariton fluid. Here, the authors show that electron–electron interactions can act to destabilize this state and lead to the formation of a modulated phase.

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.

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.

What makes the phonons in cuprates become chiral, as measured by their thermal Hall effect, is an unresolved question. Here, the authors rule out two extrinsic mechanisms and argue that chirality comes from a coupling of acoustic phonons to the intrinsic excitations of the CuO₂ planes.

The accidental band-crossing origin of Weyl nodes paired with the absence of sizeable band gaps hampers the exploitation of low-energy relativistic quasiparticles in Weyl semimetals. In a gate-tunable high-quality tellurene film, quantum Hall measurements unveil a topologically non-trivial π Berry phase caused by unconventional Weyl nodes in these tellurium two-dimensional sheets.

This allows versatile non-volatile tuning of the mutual synchronization of chains of up to four oscillators and provides a path toward individual oscillator control in large oscillatory arrays.

A strong Hall effect is observed in a material with spin textures and strong electron correlations. This hints that correlation effects can amplify real-space topological spin transport.

Imaging studies show that topological protection in the quantum Hall state in graphene is undermined by edge reconstruction with a dissipation mechanism that comprises two distinct and spatially separated processes—work generation and entropy generation.

Not only the area of Néel skyrmions, but also their number and sign contribute to their Hall resistivity.

Quantum Hall phases have chiral edge modes, which could be used to explore and exploit the quantum properties of electrons. Interactions in these edge states lead to relaxation and decoherence, hindering any realistic exploitation. Here the authors observe spectroscopically the decay and revival of the excitation created by injection of an electron into the edge mode. Their results confirm phase-coherent transport and quantify the effect of dissipation-induced decoherence.

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

Spin Hall nano-oscillators can be tuned via magnetic fields and the drive current, but individual oscillator control in large arrays remains a challenge. Here, the authors provide individual control of the threshold current and the auto-oscillation frequency by voltage-controlled magnetic anisotropy.

Conductance quantization is the hallmark of non-interacting confined systems. The authors show that the quantization in graphene nanoconstrictions with low edge disorder is suppressed in the quantum Hall regime. This is explained by the addition of new conductance channels due to electrostatic screening.

Topologically protected pseudospin transport is difficult to implement for bosonic systems due to the lack of symmetry-protected pseudospins. Here, Bleu et al. propose robust valley pseudospin transport, truly topologically protected by the winding of a quantum vortex propagating between two staggered honeycomb lattices.

Large-area graphene devices synthesized by chemical vapour deposition are used to develop electrical resistance standards, based on the quantum Hall effect, with state-of-the-art accuracy and under an extended range of experimental conditions of magnetic field, temperature and current.

A Josephson junction with a weak link made of the quantum spin Hall insulator HgTe shows evidence of topological superconductivity in response to an a.c. excitation.

Propagating spin waves known as magnons are expected to carry a dipole moment in the quantum Hall regime. Now, this moment has been detected, demonstrating that the degrees of freedom of spin and charge are entangled in quantum Hall magnons.