Weyl semimetals in three-dimensional crystals provide the paradigm example of topologically protected band nodes. It is usually taken for granted that a pair of colliding Weyl points annihilate whenever they carry opposite chiral charge. In stark contrast, here we report that Weyl points in systems that are symmetric under the composition of time reversal with a π rotation are characterized by a non-Abelian

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

This month, a Focus issue highlights recent developments in fundamental research on superconductivity.

When you start tearing a piece of aluminium foil apart, you create dislocations in the material. Suhas Eswarappa Prameela and Tim Weihs recount the story of the Burgers vector that is now an indispensable tool for describing dislocations.

Squeezed light is useful for metrology and quantum information. An optomechanical squeezed light source that works at room temperature will facilitate the technological applications of quantum light.

Topological superconductivity can emerge from the combination of conventional superconductivity in a metal and strong spin–orbit coupling in a semiconductor when they are made into a hybrid device. The most exciting manifestation of topological superconductivity is the Majorana zero modes that are predicted to exist at the ends of the proximatized nanowires. In this Perspective, we review the evidence

Squeezed light—light with quantum noise lower than shot noise in some quadratures and higher in others—can be used to improve the sensitivity of precision measurements. In particular, squeezed light sources based on nonlinear optical crystals are being used to improve the sensitivity of gravitational wave detectors. In optomechanical squeezers, the radiation-pressure-driven interaction of a coherent

The Bardeen–Cooper–Schrieffer theory of superconductivity and the Landau–Fermi liquid theory form the basis of our current understanding of conventional superconductors and their parent non-superconducting phases. However, some exotic superconductors do not conform to this physical picture but instead feature an unusual ‘normal’ state that is not a Fermi liquid. One explanation of this unusual behaviour

In order to understand the emergence of superconductivity it is useful to study the reverse process and identify the various pathways that lead to its destruction. One way is to increase the amount of disorder, as this leads to an increase in Coulomb repulsion that overpowers the attractive interaction responsible for Cooper pair formation. A second pathway—applicable to uniformly disordered materials—is

Near-term quantum computations are susceptible to noise that — left uncorrected — can destroy the correlations responsible for quantum computational speedups. New work develops tools for bolstering the noise resilience of these speedups.

As increasingly sophisticated prototypes of quantum computers are being developed, a pressing challenge is to find computational problems that can be solved by an intermediate-scale quantum computer, but are beyond the capabilities of existing classical computers. Previous work in this direction has introduced computational problems that can be solved with certainty by quantum circuits of depth independent

Twisting or sliding two-dimensional crystals with respect to each other gives rise to moiré patterns determined by the difference in their periodicities. Such lattice mismatches can exist for several reasons: differences between the intrinsic lattice constants of the two layers, as is the case for graphene on BN1; rotations between the two lattices, as is the case for twisted bilayer graphene2; and

The crystal structure of a material creates a periodic potential that electrons move through giving rise to its electronic band structure. When two-dimensional materials are stacked, the resulting moiré pattern introduces an additional periodicity so that the twist angle between the layers becomes an extra degree of freedom for the resulting heterostructure. As this angle changes, the electronic band

The second law of thermodynamics points to the existence of an ‘arrow of time’, along which entropy only increases. This arises despite the time-reversal symmetry (TRS) of the microscopic laws of nature. Within quantum theory, TRS underpins many interesting phenomena, most notably topological insulators1,2,3,4 and the Haldane phase of quantum magnets5,6. Here, we demonstrate that such TRS-protected

Readout and control of electrostatically confined electrons in semiconductors are key primitives of quantum information processing with solid-state spin qubits1,2. In superconductor–semiconductor heterostructures, localized electronic modes known as Andreev levels result from confinement that is provided by the pair potential3,4. Unlike electronic modes confined exclusively via electrostatic effects

Eukaryotic cell processes depend on molecular motors to transport cargo along cytoskeletal filaments, and the response of these mechanoenzymes to external forces shapes their cellular function. These responses have been largely mapped out in dilute, in vitro media. The cytosol, however, is host to a high concentration of macromolecules, and this crowding can alter protein conformation, binding rates

The nature of the pseudogap phase of hole-doped cuprate superconductors is still not understood fully. Several experiments have suggested that this phase ends at a critical hole doping level p*, but the nature of the ground state for lower doping is still debated. Here, we use local nuclear magnetic resonance and bulk ultrasound measurements to show that, once competing effects from superconductivity

Novel non-equilibrium phases of matter have recently become the focus of intense interest. The realization of topological phases which cannot exist under the constraints of thermodynamic equilibrium is a key aim.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Everybody who has ever made a paper airplane and been disappointed as it spins out of control, crashing to the ground, knows how tricky achieving suitable trim and stability for gliding can be. But, somehow, wiggling flying snakes glide without tumbling.

Coherent control via periodic modulation, also known as Floquet engineering, has emerged as a powerful experimental method for the realization of novel quantum systems with exotic properties. In particular, it has been employed to study topological phenomena in a variety of different platforms. In driven systems, the topological properties of the quasienergy bands can often be determined by standard

When flying snakes glide, they use aerial undulation. To determine if aerial undulation is a flight control strategy or a non-functional behavioural vestige of lateral undulation, we measured snake glides using high-speed motion capture and developed a new dynamical model of gliding. Reconstructions of the snake’s wing-body reveal that aerial undulation is composed of horizontal and vertical waves

Kerr-type nonlinearities form the basis for our physical understanding of nonlinear optical phenomena in condensed matter, such as self-focusing, solitary waves and wave mixing1,2,3. In strong fields, they are complemented by higher-order nonlinearities that enable high-harmonic generation, which is currently understood as the interplay of light-driven intraband charge dynamics and interband recombination4

In two-dimensional layered quantum materials, the stacking order of the layers determines both the crystalline symmetry and electronic properties such as the Berry curvature, topology and electron correlation1,2,3,4. Electrical stimuli can influence quasiparticle interactions and the free-energy landscape5,6, making it possible to dynamically modify the stacking order and reveal hidden structures that

Nd2Ir2O7 is a correlated semimetal with the pyrochlore structure, in which competing spin–orbit coupling and electron–electron interactions are believed to induce a time-reversal symmetry-broken Weyl semimetal phase characterized by pairs of topologically protected Dirac points at the Fermi energy1,2,3,4. However, the emergent properties in these materials are far from clear, and exotic new states

Measurement of the ground-state spin polarization of quantum systems offers great potential for the discovery and characterization of correlated electronic states. However, spin polarization measurements have mainly involved optical1,2,3 and NMR4,5 techniques that perturb the delicate ground states and, for quantum Hall systems, have provided conflicting results1,4,6. Here we present spin-resolved

An elegant experiment showing that acoustic waves are amplified after scattering by a rotating body demonstrates an effect predicted in 1971 by Yakov Zel’dovich. This result has implications for the understanding of scattering from black holes.

Experiments show how the magnetic order in antiferromagnets can be manipulated through lattice vibrations excited by a laser. This induces a large and reversible magnetic moment at very high speed.

In 1971, Zel’dovich predicted that quantum fluctuations and classical waves reflected from a rotating absorbing cylinder will gain energy and be amplified. This concept, which is a key step towards the understanding that black holes may amplify quantum fluctuations, has not been verified experimentally owing to the challenging experimental requirement that the cylinder rotation rate must be larger

Strain engineering is widely used to manipulate the electronic and magnetic properties of complex materials. For example, the piezomagnetic effect provides an attractive route to control magnetism with strain. In this effect, the staggered spin structure of an antiferromagnet is decompensated by breaking the crystal field symmetry, which induces a ferrimagnetic polarization. Piezomagnetism is especially

Predicting the properties of complex, large-scale quantum systems is essential for developing quantum technologies. We present an efficient method for constructing an approximate classical description of a quantum state using very few measurements of the state. This description, called a ‘classical shadow’, can be used to predict many different properties; order \({\mathrm{log}}\,(M)\) measurements

Quantum Hall systems are characterized by quantization of the Hall conductance—a bulk property rooted in the topological structure of the underlying quantum states1. In condensed matter devices, material imperfections hinder a direct connection to simple topological models2,3. Artificial systems, such as photonic platforms4 or cold atomic gases5, open novel possibilities by enabling specific probes

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Quantum cascade lasers are bright and compact semiconductor lasers that emit light in the mid- to far-infrared spectral region. The use of a closed ring cavity has now set them on the path towards ultrafast pulses.

Living organisms use stingers that vary in length L over eight orders of magnitude, from a few tens of nanometres to several metres, across a wide array of biological taxa. Despite the extreme variation in size, their structures are strikingly similar. However, the mechanism responsible for this remarkable morphological convergence remains unknown. Using basic physical arguments and biomimetic experiments

On the fundamental level, quantum fluctuations or entanglement lead to complex dynamical behaviour in many-body systems1 for which a description as emergent phenomena can be found within the framework of quantum field theory. A central quantity in these efforts, containing all information about the measurable physical properties, is the quantum effective action2. Though non-equilibrium quantum dynamics

Humans communicate using systems of interconnected stimuli or concepts—from language and music to literature and science—yet it remains unclear how, if at all, the structure of these networks supports the communication of information. Although information theory provides tools to quantify the information produced by a system, traditional metrics do not account for the inefficient ways that humans process

Since the 1950s, international cooperation has been the driving force behind fusion research. Here, we discuss how the International Atomic Energy Agency has shaped the field and the events that have produced fusion’s global signature partnership.

A laser–plasma experiment has recreated shock waves in collisionless, weakly magnetized conditions and evidenced electron acceleration to relativistic energies, offering unprecedented insight into a long-standing problem in astrophysics.

Microscopic motile cilia, beating in synchrony across large scales, move the liquid lining of our lungs, protecting from infection and dirt. Surprisingly, a disordered arrangement of cilia, as observed in nature, is shown to be optimal for airway clearance.

To reach their full potential, quantum computers need to be resilient to noise and decoherence. In such a fault-tolerant quantum computer, errors must be corrected in real time to prevent them from propagating between components1,2. This requirement is especially pertinent while applying quantum gates, where the interaction between components can cause errors to spread quickly throughout the system

Mucus clearance constitutes the primary defence of the respiratory system against viruses, bacteria and environmental insults. This transport across the entire airway emerges from the integrated activity of thousands of multiciliated cells, each containing hundreds of cilia, which together must coordinate their spatial arrangement, alignment and motility. The mechanisms of fluid transport have been

Astrophysical collisionless shocks are among the most powerful particle accelerators in the Universe. Generated by violent interactions of supersonic plasma flows with the interstellar medium, supernova remnant shocks are observed to amplify magnetic fields1 and accelerate electrons and protons to highly relativistic speeds2,3,4. In the well-established model of diffusive shock acceleration5, relativistic

As a unit for enzyme activity, the katal is enigmatic but struggles to find widespread acceptance. Soumitra Athavale tells its story.

The mystery of the hidden-order phase in the correlated electron paramagnet URu2Si2 is still unsolved. To address this problem, one strategy is to search for clues in the subtle competition between this state and neighbouring magnetically ordered states. It is now well established that long-range antiferromagnetic order can be stabilized in this metal when it is under pressure and that a spin-density

The contribution of partners and families to scientists’ work is often overlooked. It should be acknowledged and supported more.

The realization of quantum error correction is an essential ingredient for reaching the full potential of fault-tolerant universal quantum computation. Using a range of different schemes, logical qubits that are resistant to errors can be redundantly encoded in a set of error-prone physical qubits. One such scalable approach is based on the surface code. Here we experimentally implement its smallest

The study of the laws of nature has traditionally been pursued in the limit of isolated systems, where energy is conserved. This is not always a valid approximation, however, as the inclusion of features such as gain and loss, or periodic driving, qualitatively amends these laws. A contemporary frontier of metamaterial research is the challenge open systems pose to the characterization of topological

When two sheets of graphene are stacked on top of each other with a small twist of angle θ ≈ 1.1° between them, theory predicts the formation of a flat electronic band1,2. Experiments have shown correlated insulating, superconducting and ferromagnetic states when the flat band is partially filled3,4,5,6,7,8. The proximity of superconductivity to correlated insulators suggested a close relationship

The ability to control strongly interacting light quanta (photons) is of central importance in quantum science and engineering1,2,3,4,5. Recently it was shown that such strong interactions can be engineered in specially prepared quantum optical systems6,7,8,9,10. Here, we demonstrate a method for coherent control of strongly interacting photons, extending quantum nonlinear optics into the domain of

In the last two decades the anti-de Sitter/conformal field theory (AdS/CFT) correspondence has emerged as a focal point of many research interests. In particular, it functions as a stepping stone to a still-missing full quantum theory of gravity. In this context, a pivotal question is if and how cosmological physics can be studied using AdS/CFT. Motivated by string theory, braneworld cosmologies propose

The theory governing the strong nuclear force—quantum chromodynamics—predicts that at sufficiently high energy densities, hadronic nuclear matter undergoes a deconfinement transition to a new phase of quarks and gluons1. Although this has been observed in ultrarelativistic heavy-ion collisions2,3, it is currently an open question whether quark matter exists inside neutron stars4. By combining astrophysical

Collective processes in plasmas often induce microinstabilities that play an important role in many space or laboratory plasma environments. Particularly notable is the Weibel-type current filamentation instability, which is believed to drive the creation of collisionless shocks in weakly magnetized astrophysical plasmas. Here, this instability class is studied through interactions of ultraintense

Conduction through materials crucially depends on how ordered the materials are. Periodically ordered systems exhibit extended Bloch waves that generate metallic bands, whereas disorder is known to limit conduction and localize the motion of particles in a medium1,2. In this context, quasiperiodic systems, which are neither periodic nor disordered, demonstrate exotic conduction properties, self-similar

Highly sensitive phase- and frequency-resolved detection of microwave electric fields is of central importance in a wide range of fields, including cosmology1,2, meteorology3, communication4 and microwave quantum technology5. Atom-based electrometers6,7 promise traceable standards for microwave electrometry, but their best sensitivity is currently limited to a few μV cm−1 Hz−1/2 (refs. 8,9) and they

Automated learning from data by means of deep neural networks is finding use in an ever-increasing number of applications, yet key theoretical questions about how it works remain unanswered. A physics-based approach may help to bridge this gap.

The COVID-19 pandemic has been a sobering reminder of the extensive damage brought about by epidemics, phenomena that play a vivid role in our collective memory, and that have long been identified as significant sources of risk for humanity. The use of increasingly sophisticated mathematical and computational models for the spreading and the implications of epidemics should, in principle, provide policy-

In quantum optics, great effort is being invested in enhancing the interaction of quantum emitters with light. The different approaches include increasing the number of emitters, the laser intensity or the local photonic density of states at the location of an atom-like localized emitter. In contrast, solid-state extended emitters hold an unappreciated promise of vastly greater enhancements through

An understanding of the missing antinodal electronic excitations in the pseudogap state is essential for uncovering the physics of the underdoped cuprate high-temperature superconductors1,2,3,4,5,6. The majority of high-temperature experiments performed thus far, however, have been unable to discern whether the antinodal states are rendered unobservable due to their damping or whether they vanish due

Trapped neutral atoms have become a prominent platform for quantum science, where entanglement fidelity records have been set using highly excited Rydberg states. However, controlled two-qubit entanglement generation has so far been limited to alkali species, leaving the exploitation of more complex electronic structures as an open frontier that could lead to improved fidelities and fundamentally different