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Over the past 20 years, many efforts have been made to understand and control decoherence in 2D electron systems. In particular, several types of electronic interferometers have been considered in GaAs heterostructures, in order to protect the interfering electrons from decoherence. Nevertheless, it is now understood that several intrinsic decoherence sources fundamentally limit more advanced quantum manipulations. Here, we show that graphene offers a unique possibility to reach a regime where the decoherence is frozen and to study unexplored regimes of electron interferometry. We probe the decoherence of electron channels in a graphene quantum Hall PN junction, forming a Mach-Zehnder interferometer 1 , 2 , and unveil a scaling behavior of decay of the interference visibility with the temperature scaled by the interferometer length. It exhibits a remarkable crossover from an exponential decay at higher temperature to an algebraic decay at lower temperature where almost no decoherence occurs, a regime previously unobserved in GaAs interferometers. Quantum Hall edge channels provide a platform to study electron interference, however understanding decoherence in these systems remains an open problem. Jo et al. realize a regime of suppressed decoherence in an electronic Mach-Zehnder interferometer formed in a graphene quantum Hall pn junction.

Topological waveguides with arbitrary pathway are desirable for many applications. In this paper we construct a triangular compound lattice consisting of magnetic dielectric rods. By breaking the space symmetry and the time-reversal symmetry, the structure generates topological edge states (TESs) from the hybrid quantum Hall effects and valley Hall effects. This topological edge waveguide pathway can be arbitrary arranged just by the external magnetic field. The hybrid topological phase provides a new and ultraflexible way to the reconfiguration of the TESs.

Of the two stable forms of graphite, hexagonal and rhombohedral, the former is more common and has been studied extensively. The latter is less stable, which has so far precluded its detailed investigation, despite many theoretical predictions about the abundance of exotic interaction-induced physics 1 – 6 . Advances in van der Waals heterostructure technology 7 have now allowed us to make high-quality rhombohedral graphite films up to 50 graphene layers thick and study their transport properties. Here we show that the bulk electronic states in such rhombohedral graphite are gapped 8 and, at low temperatures, electron transport is dominated by surface states. Because of their proposed topological nature, the surface states are of sufficiently high quality to observe the quantum Hall effect, whereby rhombohedral graphite exhibits phase transitions between a gapless semimetallic phase and a gapped quantum spin Hall phase with giant Berry curvature. We find that an energy gap can also be opened in the surface states by breaking their inversion symmetry by applying a perpendicular electric field. Moreover, in rhombohedral graphite thinner than four nanometres, a gap is present even without an external electric field. This spontaneous gap opening shows pronounced hysteresis and other signatures characteristic of electronic phase separation, which we attribute to emergence of strongly correlated electronic surface states. High-quality rhombohedral graphite films are found to offer an alternative to twisted bilayer graphene as a platform for studying correlated physics in carbon materials.

An important development in the field of the fractional quantum Hall effect was the proposal that the 5/2 state observed in the Landau level with orbital index n = 1 of two-dimensional electrons in a GaAs quantum well1 originates from a chiral p-wave paired state of composite fermions that are topological bound states of electrons and quantized vortices. The excitations of this state, which is theoretically described by a ‘Pfaffian’ wavefunction2 or its hole partner called the anti-Pfaffian3,4, are neither fermions nor bosons but Majorana quasiparticles obeying non-Abelian braid statistics5. This has inspired ideas for fault-tolerant topological quantum computation6 and has also instigated a search for other states with exotic quasiparticles. Here we report experiments on monolayer graphene that show clear evidence for unexpected even denominator fractional quantum Hall physics in the n = 3 Landau level. We numerically investigate the known candidate states for the even denominator fractional quantum Hall effect, including the Pfaffian, the particle–hole symmetric Pfaffian and the 221-parton states, and conclude that, among these, the 221-parton appears a potentially suitable candidate to describe the experimentally observed state. Like the Pfaffian, this state is believed to harbour quasi-particles with non-Abelian braid statistics7.

The quantum Hall effect under the influence of gravity and inertia is studied in a unified way. We make use of an algebraic approach, as opposed to an analytic approach. We examine how both the integer and the fractional quantum Hall effects behave under a combined influence of gravity and inertia using a unified Hamiltonian. For that purpose, we first re-derive, using the purely algebraic method, the energy spectrum of charged particles moving in a plane perpendicular to a constant and uniform magnetic field either (i) under the influence of a nonlinear gravitational potential or (ii) under the influence of a constant rotation. The general Hamiltonian for describing the combined effect of gravity, rotation and inertia on the electrons of a Hall sample is then built and the eigenstates are obtained. The electrons mutual Coulomb interaction that gives rise to the familiar fractional quantum Hall effect is also discussed within such a combination.

The interplay between novel topological states and superconductivity has garnered substantial interest due to its potential for topological quantum computing. The Josephson effect serves as a useful probe for edge superconductivity in these hybrid topological materials. In Josephson junctions based on topological materials, supercurrents exhibit unique quantum interference patterns, including the conventional Fraunhofer oscillations, the Φ 0 -periodic oscillation, and the 2Φ 0 -periodic oscillation in response to the external magnetic field (Φ 0 = h /2 e is the flux quantum, h the Planck constant, and e the electron charge). These interference patterns stem from varied Andreev reflection mechanisms and the associated current density profiles. This review seeks to comprehensively examine the theoretical and experimental advancements in understanding the quantum interference patterns of edge supercurrents in Josephson junctions based on quantum spin Hall, quantum Hall, and quantum anomalous Hall systems.

We construct high-quality graphene-based van der Waals devices with narrow superconducting niobium nitride (NbN) electrodes, in which superconductivity and a robust fractional quantum Hall (FQH) state coexist. We find a possible signature for crossed Andreev reflection (CAR) across the superconductor separating two FQH edges. Our observed CAR probabilities in the particlelike fractional fillings are markedly higher than those in the integer and hole-conjugate fractional fillings and depend strongly on temperature and magnetic field unlike the other fillings. Further, we find a filling-independent CAR probability in integer fillings, which we attribute to spin-orbit coupling in NbN allowing for Andreev reflection between spin-polarized edges. These results provide a route to realize novel topological superconducting phases in FQH-superconductor hybrid devices based on graphene and NbN.

Quantum devices characterized by non-Hermitian topology are predicted to show highly robust and potentially useful properties for precision sensing and signal amplification. However, realizing them has remained a daunting experimental task, as non-Hermiticity is often associated with gain and loss, which would require precise tailoring to produce the signatures of non-trivial topology. Here, instead of gain and loss, we use the non-reciprocity of quantum Hall edge states to directly observe non-Hermitian topology in a multi-terminal quantum Hall ring. Our transport measurements evidence a robust, non-Hermitian skin effect, characterized by currents and voltages showing an exponential profile that persists across Hall plateau transitions away from the regime of maximum non-reciprocity. Our observation of non-Hermitian topology in a quantum device introduces a scalable experimental approach to construct and investigate generic non-Hermitian systems. Non-Hermitian systems can be described in terms of gain and loss with a coupled environment—a hard feature to tune in quantum devices. Now an experiment shows non-Hermitian topology in a quantum Hall ring without relying on gain and loss.

Two-dimensional semiconductors, such as transition metal dichalcogenides, have demonstrated tremendous promise for the development of highly tunable quantum devices. Realizing this potential requires low-resistance electrical contacts that perform well at low temperatures and low densities where quantum properties are relevant. Here we present a new device architecture for two-dimensional semiconductors that utilizes a charge-transfer layer to achieve large hole doping in the contact region, and implement this technique to measure the magnetotransport properties of high-purity monolayer WSe 2 . We measure a record-high hole mobility of 80,000 cm 2  V –1  s –1 and access channel carrier densities as low as 1.6 × 10 11  cm −2 , an order of magnitude lower than previously achievable. Our ability to realize transparent contact to high-mobility devices at low density enables transport measurements of correlation-driven quantum phases including the observation of a low-temperature metal–insulator transition in a density and temperature regime where Wigner crystal formation is expected and the observation of the fractional quantum Hall effect under large magnetic fields. The charge-transfer contact scheme enables the discovery and manipulation of new quantum phenomena in two-dimensional semiconductors and their heterostructures. By utilizing the van der Waals electron acceptor α-RuCl 3 , this study establishes a p-type connection with WSe 2 , facilitating a high hole mobility of 80,000 cm 2  V –1  s –1 for investigating quantum transport properties in a magnetic field of over 30 T.

Electronic band structures dictate the mechanical, optical and electrical properties of crystalline solids. Their experimental determination is therefore crucial for technological applications. Although the spectral distribution in energy bands is routinely measured by various techniques 1 , it is more difficult to access the topological properties of band structures such as the quantized Berry phase, γ , which is a gauge-invariant geometrical phase accumulated by the wavefunction along an adiabatic cycle 2 . In graphene, the quantized Berry phase γ  = π accumulated by massless relativistic electrons along cyclotron orbits is evidenced by the anomalous quantum Hall effect 4 , 5 . It is usually thought that measuring the Berry phase requires the application of external electromagnetic fields to force the charged particles along closed trajectories 3 . Contradicting this belief, here we demonstrate that the Berry phase of graphene can be measured in the absence of any external magnetic field. We observe edge dislocations in oscillations of the charge density ρ (Friedel oscillations) that are formed at hydrogen atoms chemisorbed on graphene. Following Nye and Berry 6 in describing these topological defects as phase singularities of complex fields, we show that the number of additional wavefronts in the dislocation is a real-space measure of the Berry phase of graphene. Because the electronic dispersion relation can also be determined from Friedel oscillations 7 , our study establishes the charge density as a powerful observable with which to determine both the dispersion relation and topological properties of wavefunctions. This could have profound consequences for the study of the band-structure topology of relativistic and gapped phases in solids. The Berry phase of graphene is measured in the absence of an applied magnetic field by observing dislocations in the Friedel oscillations formed at a hydrogen atom adsorbed on graphene.