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  • The recent discovery of higher-order band topology in topological insulators has unveiled the hierarchical structure of topological band theory. This Perspective reviews this rapidly developing field and discusses future directions, including open challenges, future trends, synergy and its use in other fields and potential applications.

    • Biye Xie
    • Hai-Xiao Wang
    • Yanfeng Chen
  • Experiments suggest that graphene systems with moiré potentials exhibit orbital magnetism. This Perspective discusses the experimental evidence and introduces theoretical perspectives on the phenomena.

    • Jianpeng Liu
    • Xi Dai
  • Complexity economics relaxes the assumptions of neoclassical economics to assume that agents differ, that they have imperfect information about other agents and they must, therefore, try to make sense of the situation they face. This Perspective sketches the ideas of complexity economics and describes how it links to complexity science more broadly.

    • W. Brian Arthur
  • Designing new experiments in physics is a challenge for humans; therefore, computers have become a tool to expand scientists’ capabilities and to provide creative solutions. This Perspective article examines computer-inspired designs in quantum physics that led to laboratory experiments and inspired new scientific insights.

    • Mario Krenn
    • Manuel Erhard
    • Anton Zeilinger
  • Magnetic skyrmions, two-dimensional nanometre-scale localized states, are promising candidates for new technological applications. This Perspective surveys the progress in this field and offers a brief, accessible guide to the basic physical principles of magnetic skyrmions.

    • Alexei N. Bogdanov
    • Christos Panagopoulos
  • Neuromorphic computing takes inspiration from the brain to create energy-efficient hardware for information processing, capable of highly sophisticated tasks. Including more physics in the algorithms and nanoscale materials used for computing could have a major impact in this field.

    • Danijela Marković
    • Alice Mizrahi
    • Julie Grollier
  • Droplets in general are multicomponent and experience gradients in concentration, often leading to transport phenomena and phase transitions. This Perspective discusses recent progress on the physicochemical hydrodynamics of such droplet systems and their relevance for many important applications.

    • Detlef Lohse
    • Xuehua Zhang
  • Non-line-of-sight (NLOS) imaging methods use light scattered from multiple surfaces to reconstruct images of scenes that are hidden by another object. This Perspective summarizes existing NLOS imaging techniques and discusses which directions show most promise for future developments.

    • Daniele Faccio
    • Andreas Velten
    • Gordon Wetzstein
  • Due to their atomic structure, ultracold alkaline-earth atoms are well suited for quantum simulation and the study of quantum many-body physics. This Perspective overviews the ways to control the interactions between atoms and discusses the new physics that could be uncovered.

    • Ren Zhang
    • Yanting Cheng
    • Hui Zhai
  • Substantial progress has been made towards making fusion a source of commercial energy. One challenge is the damage that filamentary plasma eruptions cause to plasma-facing components. This Perspective summarizes what is understood about these eruptions and strategies for controlling them.

    • Christopher Ham
    • Andrew Kirk
    • Howard Wilson
  • The dynamics of quantum information is opening new perspectives on the behaviour of complex many-body systems. This Perspective covers progress made with atomic gases and trapped ions for accessing the dynamics of quantum correlations, entanglement and information scrambling in a broad parameter regime.

    • R. J. Lewis-Swan
    • A. Safavi-Naini
    • A. M. Rey
  • Electric dipole moments (EDMs) of atoms and molecules are a sensitive probe for sources of time-reversal symmetry violation beyond the standard model. In this Perspective, we review recent progress in EDM searches with atoms and molecules and survey proposed next-generation experiments.

    • William B. Cairncross
    • Jun Ye
  • Although the differential equations that describe the physical climate system are deterministic, there are reasons, both theoretical and practical, why computational representations of these equations should be stochastic. This Perspective surveys the benefits of stochastic modelling of weather and climate.

    • T. N. Palmer
  • This Perspective describes how statistical physics helps understand some of the key aspects of cities: their spatial structure and social organization, the distribution of their population, urban mobility and how some critical factors vary with population.

    • Marc Barthelemy
  • Synthetic dimensions provide a way to artificially engineer extra spatial dimensions through other degrees of freedom. We review how synthetic dimensions have emerged as a promising tool for quantum simulations of topological lattice models in atomic, molecular and optical systems.

    • Tomoki Ozawa
    • Hannah M. Price
  • An analysis of the number of physicists and their career paths reveals the changing landscape of the physics subdisciplines, highlighting the connections between different fields and the effects of large collaborations.

    • Federico Battiston
    • Federico Musciotto
    • Roberta Sinatra