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Abstract Topological photonics seeks to control the behaviour of the light through the design of protected topological modes in photonic structures. While this approach originated from studying the behaviour of electrons in solid-state materials, it has since blossomed into a field that is at the very forefront of the search for new topological types of matter. This can have real implications for future technologies by harnessing the robustness of topological photonics for applications in photonics devices. This roadmap surveys some of the main emerging areas of research within topological photonics, with a special attention to questions in fundamental science, which photonics is in an ideal position to address. Each section provides an overview of the current and future challenges within a part of the field, highlighting the most exciting opportunities for future research and developments. 

Abstract A variety of precise experiments have been carried out to establish the character of the superconducting state in Sr 2 RuO 4 . Many of these appear to imply contradictory conclusions concerning the symmetries of this state. Here we propose that these results can be reconciled if we assume that there is a near-degeneracy between a $${d}_{{x}^{2}-{y}^{2}}$$ d x 2 − y 2 (B 1 g in group theory nomenclature) and a $${g}_{xy({x}^{2}-{y}^{2})}$$ g x y ( x 2 − y 2 ) (A 2 g ) superconducting state. From a weak-coupling perspective, such an accidental degeneracy can occur at a point at which a balance between the on-site and nearest-neighbor repulsions triggers a d -wave to g -wave transition. 

Quantum materials represent one of the most promising frontiers in the quest for faster, lightweight, energy-efficient technologies. However, their inherent complexity and rich phase landscape make them challenging to understand or manipulate. Here, we present a new ultrafast electron calorimetry technique that can systematically uncover new phases of quantum matter. Using time- and angle-resolved photoemission spectroscopy, we measure the dynamic electron temperature, band structure, and heat capacity. This approach allows us to uncover a new long-lived metastable state in the charge density wave material 1 T -TaSe 2 , which is distinct from all the known equilibrium phases: It is characterized by a substantially reduced effective total heat capacity that is only 30% of the normal value, because of selective electron-phonon coupling to a subset of phonon modes. As a result, less energy is required to melt the charge order and transform the state of the material than under thermal equilibrium conditions.