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The electronic band structure of van der Waals (vdW) layered crystals has properties that depend on the composition, thickness and stacking of the component layers. Here we use density functional theory and high field magneto-optics to investigate the metal chalcogenide InSe, a recent addition to the family of vdW layered crystals, which transforms from a direct to an indirect band gap semiconductor as the number of layers is reduced. We investigate this direct-to-indirect bandgap crossover, demonstrate a highly tuneable optical response from the near infrared to the visible spectrum with decreasing layer thickness down to 2 layers, and report quantum dot-like optical emissions distributed over a wide range of energy. Our analysis also indicates that electron and exciton effective masses are weakly dependent on the layer thickness and are significantly smaller than in other vdW crystals. These properties are unprecedented within the large family of vdW crystals and demonstrate the potential of InSe for electronic and photonic technologies.

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.

Optical metasurfaces have raised immense expectations as cheaper and lighter alternatives to bulk optical components. In recent years, novel components combining multiple optical functions have been proposed pushing further the level of requirement on the manufacturing precision of these objects. In this work, we study in details the influence of the most common fabrication errors on the optical response of a metasurface and quantitatively assess the tolerance to fabrication errors based on extensive numerical simulations. We illustrate these results with the design, fabrication and characterization of a silicon nanoresonator-based metasurface that operates as a beam deflector in the near-infrared range.

Two-dimensional systems can host exotic particles called anyons whose quantum statistics are neither bosonic nor fermionic. For example, the elementary excitations of the fractional quantum Hall effect at filling factor ν = 1/m (where m is an odd integer) have been predicted to obey Abelian fractional statistics, with a phase ϕ associated with the exchange of two particles equal to π/m. However, despite numerous experimental attempts, clear signatures of fractional statistics have remained elusive. We experimentally demonstrate Abelian fractional statistics at filling factor ν = ⅓ by measuring the current correlations resulting from the collision between anyons at a beamsplitter. By analyzing their dependence on the anyon current impinging on the splitter and comparing with recent theoretical models, we extract ϕ = π/3, in agreement with predictions.

Current flow in electronic devices can be asymmetric with bias direction, a phenomenon underlying the utility of diodes 1 and known as non-reciprocal charge transport 2 . The promise of dissipationless electronics has recently stimulated the quest for superconducting diodes, and non-reciprocal superconducting devices have been realized in various non-centrosymmetric systems 3 – 10 . Here we investigate the ultimate limits of miniaturization by creating atomic-scale Pb–Pb Josephson junctions in a scanning tunnelling microscope. Pristine junctions stabilized by a single Pb atom exhibit hysteretic behaviour, confirming the high quality of the junctions, but no asymmetry between the bias directions. Non-reciprocal supercurrents emerge when inserting a single magnetic atom into the junction, with the preferred direction depending on the atomic species. Aided by theoretical modelling, we trace the non-reciprocity to quasiparticle currents flowing by means of electron–hole asymmetric Yu–Shiba–Rusinov states inside the superconducting energy gap and identify a new mechanism for diode behaviour in Josephson junctions. Our results open new avenues for creating atomic-scale Josephson diodes and tuning their properties through single-atom manipulation. By analysing atomic-scale Pb–Pb Josephson junctions including magnetic atoms in a scanning tunnelling microscope, a new mechanism for diode behaviour is demonstrated, opening up new paths to tune their properties by means of single-atom manipulation.

The flow of water in carbon nanochannels has defied understanding thus far 1 , with accumulating experimental evidence for ultra-low friction, exceptionally high water flow rates and curvature-dependent hydrodynamic slippage 2 – 5 . In particular, the mechanism of water–carbon friction remains unknown 6 , with neither current theories 7 nor classical 8 , 9 or ab initio molecular dynamics simulations 10 providing satisfactory rationalization for its singular behaviour. Here we develop a quantum theory of the solid–liquid interface, which reveals a new contribution to friction, due to the coupling of charge fluctuations in the liquid to electronic excitations in the solid. We expect that this quantum friction, which is absent in Born–Oppenheimer molecular dynamics, is the dominant friction mechanism for water on carbon-based materials. As a key result, we demonstrate a marked difference in quantum friction between the water–graphene and water–graphite interface, due to the coupling of water Debye collective modes with a thermally excited plasmon specific to graphite. This suggests an explanation for the radius-dependent slippage of water in carbon nanotubes 4 , in terms of the electronic excitations of the nanotubes. Our findings open the way for quantum engineering of hydrodynamic flows through the electronic properties of the confining wall. The quantum contribution to friction enables the rationalization of the peculiar friction properties of water on carbon surfaces, and in particular the radius dependence of slippage in carbon nanotubes.

Interactions among electrons create novel many-body quantum phases of matter with wavefunctions that reflect electronic correlation effects, broken symmetries and collective excitations. Many quantum phases have been discovered in magic-angle twisted bilayer graphene (MATBG), including correlated insulating 1 , unconventional superconducting 2 – 5 and magnetic topological 6 – 9 phases. The lack of microscopic information 10 , 11 of possible broken symmetries has hampered our understanding of these phases 12 – 17 . Here we use high-resolution scanning tunnelling microscopy to study the wavefunctions of the correlated phases in MATBG. The squares of the wavefunctions of gapped phases, including those of the correlated insulating, pseudogap and superconducting phases, show distinct broken-symmetry patterns with a √3 × √3 super-periodicity on the graphene atomic lattice that has a complex spatial dependence on the moiré scale. We introduce a symmetry-based analysis using a set of complex-valued local order parameters, which show intricate textures that distinguish the various correlated phases. We compare the observed quantum textures of the correlated insulators at fillings of ±2 electrons per moiré unit cell to those expected for proposed theoretical ground states. In typical MATBG devices, these textures closely match those of the proposed incommensurate Kekulé spiral order 15 , whereas in ultralow-strain samples, our data have local symmetries like those of a time-reversal symmetric intervalley coherent phase 12 . Moreover, the superconducting state of MATBG shows strong signatures of intervalley coherence, only distinguishable from those of the insulator with our phase-sensitive measurements. High-resolution scanning tunnelling microscopy is used to observe the quantum textures of the many-body wavefunctions of the correlated insulating, pseudogap and superconducting phases in magic-angle graphene.

A two-mode waveguide is designed to realize a dynamical encircling of an exceptional point at which two resonances coincide in their frequency and their rate of decay; as a result the waveguide transmits only into a unique mode at either one of its two output ports. Exceptional points promise exotic prizes In physical systems with gain and loss modes, unusual behaviour can arise at so-called exceptional points where such modes coalesce. In previous work on optical systems, exceptional points have been harnessed to realize effects such as unidirectional light transmission and lasing suppression and revival. It is further predicted that slowly encircling exceptional points in parameter space induces non-reciprocal transitions between two states. This intriguing fundamental effect has now been demonstrated experimentally by two independent teams. Jack Harris and colleagues observe energy transfer between two vibrational modes in an optomechanical resonator, and Stefan Rotter and colleagues measure asymmetric mode switching in a microwave transmission line. These studies pave the way for further experimental and fundamental exploration of physical phenomena around exceptional points. Physical systems with loss or gain have resonant modes that decay or grow exponentially with time. Whenever two such modes coalesce both in their resonant frequency and their rate of decay or growth, an ‘exceptional point’ occurs, giving rise to fascinating phenomena that defy our physical intuition 1 , 2 , 3 , 4 , 5 , 6 . Particularly intriguing behaviour is predicted to appear when an exceptional point is encircled sufficiently slowly 7 , 8 , such as a state-flip or the accumulation of a geometric phase 9 , 10 . The topological structure of exceptional points has been experimentally explored 11 , 12 , 13 , but a full dynamical encircling of such a point and the associated breakdown of adiabaticity 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 have remained out of reach of measurement. Here we demonstrate that a dynamical encircling of an exceptional point is analogous to the scattering through a two-mode waveguide with suitably designed boundaries and losses. We present experimental results from a corresponding waveguide structure that steers incoming waves around an exceptional point during the transmission process. In this way, mode transitions are induced that transform this device into a robust and asymmetric switch between different waveguide modes. This work will enable the exploration of exceptional point physics in system control and state transfer schemes at the crossroads between fundamental research and practical applications.

Revealing universal behaviours is a hallmark of statistical physics. Phenomena such as the stochastic growth of crystalline surfaces 1 and of interfaces in bacterial colonies 2 , and spin transport in quantum magnets 3 – 6 all belong to the same universality class, despite the great plurality of physical mechanisms they involve at the microscopic level. More specifically, in all these systems, space–time correlations show power-law scalings characterized by universal critical exponents. This universality stems from a common underlying effective dynamics governed by the nonlinear stochastic Kardar–Parisi–Zhang (KPZ) equation 7 . Recent theoretical works have suggested that this dynamics also emerges in the phase of out-of-equilibrium systems showing macroscopic spontaneous coherence 8 – 17 . Here we experimentally demonstrate that the evolution of the phase in a driven-dissipative one-dimensional polariton condensate falls in the KPZ universality class. Our demonstration relies on a direct measurement of KPZ space–time scaling laws 18 , 19 , combined with a theoretical analysis that reveals other key signatures of this universality class. Our results highlight fundamental physical differences between out-of-equilibrium condensates and their equilibrium counterparts, and open a paradigm for exploring universal behaviours in driven open quantum systems. Experiments show that the dynamics of phase fluctuations  in a one-dimensional polariton condensate falls in the Kardar–Parisi–Zhang universality class, and theoretical analysis supports this finding revealing the key signatures of this universality class.

Topological physics relies on the structure of the eigenstates of the Hamiltonians. The geometry of the eigenstates is encoded in the quantum geometric tensor 1 —comprising the Berry curvature 2 (crucial for topological matter) 3 and the quantum metric 4 , which defines the distance between the eigenstates. Knowledge of the quantum metric is essential for understanding many phenomena, such as superfluidity in flat bands 5 , orbital magnetic susceptibility 6 , 7 , the exciton Lamb shift 8 and the non-adiabatic anomalous Hall effect 6 , 9 . However, the quantum geometry of energy bands has not been measured. Here we report the direct measurement of both the Berry curvature and the quantum metric in a two-dimensional continuous medium—a high-finesse planar microcavity 10 —together with the related anomalous Hall drift. The microcavity hosts strongly coupled exciton–photon modes (exciton polaritons) that are subject to photonic spin–orbit coupling 11 from which Dirac cones emerge 12 , and to exciton Zeeman splitting, breaking time-reversal symmetry. The monopolar and half-skyrmion pseudospin textures are measured using polarization-resolved photoluminescence. The associated quantum geometry of the bands is extracted, enabling prediction of the anomalous Hall drift, which we measure independently using high-resolution spatially resolved epifluorescence. Our results unveil the intrinsic chirality of photonic modes, the cornerstone of topological photonics 13 – 15 . These results also experimentally validate the semiclassical description of wavepacket motion in geometrically non-trivial bands 9 , 16 . The use of exciton polaritons (interacting photons) opens up possibilities for future studies of quantum fluid physics in topological systems. 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.