The interplay of different electronic phases underlies the physics of unconventional superconductors. One of the most intriguing examples is a high-temperature superconductor, FeTe1 – xSex (refs. 1,2,3,4,5,6,7,8,9,10,11). This superconductor undergoes both a topological transition3,4, linked to the electronic band inversion, and an electronic nematic phase transition, associated with rotation symmetry

The two-fluid model of superfluids predicts a second, quantum mechanical form of sound. Ultracold atom experiments have now measured second sound in the unusual two-dimensional superfluid described by the Berezinskii–Kosterlitz–Thouless transition.

Introducing non-local effects to metamaterials increases the complexity of their dispersion relation, which allows carefully designed elastic structures to mimic the peculiar roton behaviour of correlated quantum superfluids.

A single equation can describe how fluids flow across a wide range of length scales, from ocean currents to swimming algae. The difference merely lies in the Reynolds number, says Julia Yeomans.

Articulating the case for investment in large-scale physics projects is rarely straightforward. If scientists are to continue to do so effectively in the future, they must learn to grapple with a host of issues that they have perhaps been lucky to be shielded from in the past.

High-order harmonics of laser pulses yield spectral components with shorter wavelength and duration and tighter focus than the original pulse. Precise spatiotemporal characterization of this radiation from a relativistic plasma mirror is relevant for ultrafast science.

Reaching light intensities above 1025 W cm−2 and up to the Schwinger limit of order 1029 W cm−2 would enable the testing of fundamental predictions of quantum electrodynamics. A promising—yet challenging—approach to achieve such extreme fields consists in reflecting a high-power femtosecond laser pulse off a curved relativistic mirror. This enhances the intensity of the reflected beam by simultaneously

Undergraduate labs are more effective and more positive for students if they encourage investigation and decision-making, not verification of textbook concepts.

Recent measurements of observables related to proton and neutron spin properties at low energies are in disagreement with the available theoretical predictions, and continue to challenge nuclear experimentalists and theorists alike.

Understanding the nucleon spin structure in the regime where the strong interaction becomes truly strong poses a challenge to both experiment and theory. At energy scales below the nucleon mass of about 1 GeV, the intense interaction among the quarks and gluons inside the nucleon makes them highly correlated. Their coherent behaviour causes the emergence of effective degrees of freedom, requiring the

Thermalization is the inevitable fate of many complex quantum systems, whose dynamics allow them to fully explore the vast configuration space regardless of the initial state—the behaviour known as quantum ergodicity. In a quest for experimental realizations of coherent long-time dynamics, efforts have focused on ergodicity-breaking mechanisms, such as integrability and localization. The recent discovery

Gradients in fluid viscosity characterize microbiomes ranging from mucus layers on marine organisms1 and human viscera2,3 to biofilms4. Although such environments are widely recognized for their protective effects against pathogens and their ability to influence cell motility2,5, the physical mechanisms regulating cell transport in viscosity gradients remain elusive6,7,8, primarily due to a lack of

On the face of it, characterizing quantum dynamics in the exponentially large Hilbert space of a many-body system might require prohibitively many experiments. In fact, the locality of physical interactions means that it can be done efficiently.

Learning the Hamiltonian that describes interactions in a quantum system is an important task in both condensed-matter physics and the verification of quantum technologies. Its classical analogue arises as a central problem in machine learning known as learning Boltzmann machines. Previously, the best known methods for quantum Hamiltonian learning with provable performance guarantees required a number

A life-or-death choice determines the fate of reproductive cells. It has long been assumed that the choice is genetically regulated, but it now seems that the decision may instead be controlled by intracellular pressure.

A type of polar self-propelled particle generates a torque that makes it naturally drawn to higher-density areas. The collective behaviour this induces in assemblies of particles constitutes a new form of phase separation in active fluids.

Studies of active matter, from molecular assemblies to animal groups, have revealed two broad classes of behaviour: a tendency to align yields orientational order and collective motion, whereas particle repulsion leads to self-trapping and motility-induced phase separation. Here we report a third class of behaviour: orientational interactions that produce active phase separation. Combining theory and

Oocytes are large cells that develop into an embryo upon fertilization1. As interconnected germ cells mature into oocytes, some of them grow—typically at the expense of others that undergo cell death2,3,4. We present evidence that in the nematode Caenorhabditis elegans, this cell-fate decision is mechanical and related to tissue hydraulics. An analysis of germ cell volumes and material fluxes identifies

At high pressures, simple metals such as potassium have a rich phase diagram including an insulating electride phase in which electrons have a localized, anionic character. Measurements in the liquid phase have shown a transition between two states, but experimental challenges have prevented detailed thermodynamic measurements. Using potassium as an example, we present numerical evidence that the liquid–liquid

A Correction to this paper has been published: https://doi.org/10.1038/s41567-021-01261-9.

Quantum gates on trapped ions may be quicker and more reliable owing to squeezing of their vibrational motion. A threefold drop in operation time shows potential for applications in quantum technologies.

In the class of materials called spin liquids1,2,3, a magnetically ordered state cannot be attained even at millikelvin temperatures because of conflicting constraints on each spin; for example, from geometric or exchange frustration. The resulting quantum spin-liquid state is currently of intense interest because it exhibits unusual excitations as well as wave-function entanglement. The layered insulator

A major challenge in developing topological superconductors for implementing topological quantum computing is their characterization and control. It has been proposed that a p-wave-gapped topological superconductor can be fabricated with single-atom precision by assembling chains of magnetic atoms on s-wave superconductors with spin–orbit coupling. Here we analyse Bogoliubov quasiparticle interference

Strong and precisely controlled interactions between quantum objects are essential for quantum information processing1,2, simulation3 and sensing4,5, and for the formation of exotic quantum matter6. A well-established paradigm for coupling otherwise weakly interacting quantum objects is to use auxiliary bosonic quantum excitations to mediate the interactions. Important examples include photon-mediated

The recent measurement of the muon’s anomalous magnetic moment increases the tension with predictions from theory. Or does it?

As the namesake of a variety of constants, distributions and equations, Ludwig Boltzmann has earned his place in the physics hall of fame. But as Ankita Anirban reveals, he cannot take sole credit for the most famous constant bearing his name.

Robustness against perturbations lies at the heart of topological phenomena. If, however, a perturbation such as disorder becomes dominant, it may cause a topological phase transition between topologically non-trivial and trivial phases. Here we experimentally reveal the competition and interplay between topology and quasi-periodic disorder in a Thouless pump realized with ultracold atoms in an optical

As Hamiltonian models underpin the study and analysis of physical and chemical processes, it is crucial that they are faithful to the system they represent. However, formulating and testing candidate Hamiltonians for quantum systems from experimental data is difficult, because one cannot directly observe which interactions are present. Here we propose and demonstrate an automated protocol to overcome

Measurements of isotope ratios are predominantly made with reference to standard specimens that have been characterized in the past. In the 1950s, the carbon isotope ratio was referenced to a belemnite sample collected by Heinz Lowenstam and Harold Urey1 in South Carolina’s PeeDee region. Due to exhaustion of the sample since then, reference materials that are traceable to the original artefact are

Semiconductor heterostructures1 and ultracold neutral atomic lattices2 capture many of the essential properties of one-dimensional electronic systems. However, fully one-dimensional superlattices are highly challenging to fabricate in the solid state due to the inherently small length scales involved. Conductive atomic force microscope lithography applied to an oxide interface can create ballistic

The strong Ising spin–orbit coupling in certain two-dimensional transition metal dichalcogenides can profoundly affect the superconducting state in few-layer samples. For example, in NbSe2, this effect combines with the reduced dimensionality to stabilize the superconducting state against magnetic fields up to ~35 T, and could lead to topological superconductivity. Here we report a two-fold rotational

Measuring the spin structure of protons and neutrons tests our understanding of how they arise from quarks and gluons, the fundamental building blocks of nuclear matter. At long distances, the coupling constant of the strong interaction becomes large, requiring non-perturbative methods to calculate quantum chromodynamics processes, such as lattice gauge theory or effective field theories. Here we report

The physical state of embryonic tissues emerges from non-equilibrium, collective interactions among constituent cells. Cellular jamming, rigidity transitions and characteristics of glassy dynamics have all been observed in multicellular systems, but it is unclear how cells control these emergent tissue states and transitions, including tissue fluidization. Combining computational and experimental methods

Strong electronic interactions in condensed-matter systems often lead to unusual quantum phases. One such phase occurs in the Kondo insulator YbB12, the insulating state of which exhibits phenomena that are characteristic of metals, such as magnetic quantum oscillations1, a gapless fermionic contribution to heat capacity2,3 and itinerant-fermion thermal transport3. To understand these phenomena, it

The US Department of Justice’s ‘China Initiative’ is unfairly targeting Chinese American academics for their alleged ties with the Chinese government. A more proportionate approach is urgently needed.

What does it mean for an individual to be ‘important’ or for a connection to be ‘outstanding’? The answer depends on context, as Sarah Shugars and Samuel V. Scarpino explain.

Scientific progress has always been driven by the ability to build an instrument to answer a specific question. But spreading the news of how to replicate that tool is an evolving art, ripe for an open-source revolution.

Gradients in the concentration of a solute can drive particle transport by inducing interfacial flows via imbalances in the osmotic pressure near surfaces. Now it seems that this mechanism is directing traffic on the cell membrane.

Among the most actively studied issues in the cuprates are the natures of the pseudogap and strange metal states and their relationship to superconductivity1. There is general agreement that the low-energy physics of the Mott-insulating parent state is well captured by a two-dimensional spin S = 1/2 antiferromagnetic Heisenberg model2. However, recent observations of a large thermal Hall conductivity

The healthy growth and maintenance of a biological system depends on the precise spatial organization of molecules within the cell through the dissipation of energy. Reaction–diffusion mechanisms can facilitate this organization, as can directional cargo transport orchestrated by motor proteins, by relying on specific protein interactions. However, transport of material through the cell can also be

A detailed analysis of a nucleon-knockout experiment has put forward a methodological roadmap for overcoming ambiguities in the interpretation of the data — promising access to the nuclear wave functions in unstable nuclei.

The Ising chain in a transverse field is a paradigmatic model for a host of physical phenomena, including spontaneous symmetry breaking, quantum criticality and duality. Although the quasi-one-dimensional ferromagnet CoNb2O6 has been regarded as the Ising chain’s best material realization, it exhibits substantial deviations from ideality. By combining terahertz spectroscopy and calculations, we show

Particle knockout scattering experiments1,2 are fundamental for mapping the structure of atomic nuclei2,3,4,5,6, but their interpretation is often complicated by initial- and final-state interactions of the incoming and scattered particles1,2,7,8,9. Such interactions lead to reduction in the scattered particle flux and distort their kinematics. Here we overcome this limitation by measuring the quasi-free

The patterning dynamics of confined immiscible fluids has inspired an elegant and versatile approach to building periodic three-dimensional multi-material architectures. The technique extends to triphasic composites, three-dimensional droplet networks and even biological tissues.

The Earth’s magnetosphere is the outermost layer of the geospace system deflecting energetic charged particles from the Sun and solar wind. The solar wind has major impacts on the Earth’s magnetosphere, but it is unclear whether the same holds for solar flares—a sudden eruption of electromagnetic radiation on the Sun. Here we use a recently developed whole geospace model combined with observational

Structures that are periodic on a microscale in three dimensions are abundant in nature, for example, in the cellular arrays that make up living tissue. Such structures can also be engineered, appearing in smart materials1,2,3,4, photonic crystals5, chemical reactors6, and medical7 and biomimetic8 technologies. Here we report that fluid–fluid interfacial energy drives three-dimensional (3D) structure

Excitations confined by long-range interactions between Ising spins may provide a way for systems to escape thermalization. A quantum simulator made of trapped ions has now made such confinement-induced enhancement possible.

Particles subject to confinement experience an attractive potential that increases without bound as they separate. A prominent example is colour confinement in particle physics, in which baryons and mesons are produced by quark confinement. Confinement can also occur in low-energy quantum many-body systems when elementary excitations are confined into bound quasiparticles. Here we report the observation

Plasma-based accelerators driven by either intense lasers1 or charged particle beams2 can accelerate electrons or positrons with extremely high gradients compared with conventional radio-frequency accelerators. For their use as next-generation light sources and in energy frontier colliders3, beams with good stability, high quality, controllable polarization and excellent reproducibility4,5 are required

Classical hydrodynamics is a remarkably versatile description of the coarse-grained behaviour of many-particle systems once local equilibrium has been established1. The form of the hydrodynamical equations is determined primarily by the conserved quantities present in a system. Some quantum spin chains are known to possess, even in the simplest cases, a greatly expanded set of conservation laws, and

Efforts to understand the microscopic origin of superconductivity in the cuprates are dependent on knowledge of the normal state. The Hall number in the low-temperature, high-field limit nH(0) has a particular importance because, within conventional transport theory, it is simply related to the number of charge carriers, so its evolution with doping gives crucial information about the nature of the

Surface scientists love a good vacuum. The reason for this is captured by the work of Irving Langmuir and the little-known unit bearing his name, explains Daniel Payne.

A year on from the last-minute cancellation of the 2020 American Physical Society March Meeting, we examine the ups and downs of the online conference experience that has become the new normal during the COVID-19 pandemic.

Passing a supercurrent through a topological material can highlight the existence of higher-order boundary states, and may lead to applications in topological superconductivity.

A Correction to this paper has been published: https://doi.org/10.1038/s41567-021-01212-4.

The virtual photons that are exchanged when a free-electron vortex beam interacts with a nanoscopic target unlock an explicit connection between polarized optical spectroscopy and the inelastic scattering of scalar electron waves.

Spectromicroscopy techniques with fast electrons can quantitatively measure the optical response of excitations with unrivalled spatial resolution. However, owing to their inherently scalar nature, electron waves cannot access the polarization-related quantities. Despite promising attempts based on the conversion of concepts originating from singular optics (such as vortex beams), the definition of

Strontium ruthenate (Sr2RuO4) continues to present an important test of our understanding of unconventional superconductivity, because while its normal-state electronic structure is known with precision, its superconductivity remains unexplained. There is evidence that its order parameter is chiral, but reconciling this with recent observations of the spin part of the pairing requires an order parameter

A Correction to this paper has been published: https://doi.org/10.1038/s41567-021-01205-3.

Flat bands in magic-angle twisted bilayer graphene (MATBG) have recently emerged as a rich platform to explore strong correlations1, superconductivity2,3,4,5 and magnetism3,6,7. However, the phases of MATBG in a magnetic field and what they reveal about the zero-field phase diagram remain relatively uncharted. Here we report a rich sequence of wedge-like regions of quantized Hall conductance with Chern