A perspective on topological nanophotonics: Current status and future challenges

17 pags., 10 figs., 1 tab. -- Open Access funded by Creative Commons Atribution Licence 4.0Topological photonic systems, with their ability to host states protected against disorder and perturbation, allow us to do with photons what topological insulators do with electrons. Topological photonics can refer to electronic systems coupled with light or purely photonic setups. By shrinking these systems to the nanoscale, we can harness the enhanced sensitivity observed in nanoscale structures and combine this with the protection of the topological photonic states, allowing us to design photonic local density of states and to push towards one of the ultimate goals of modern science: the precise control of photons at the nanoscale. This is paramount for both nanotechnological applications and fundamental research in light matter problems. For purely photonic systems, we work with bosonic rather than fermionic states, so the implementation of topology in these systems requires new paradigms. Trying to face these challenges has helped in the creation of the exciting new field of topological nanophotonics, with far-reaching applications. In this article, we review milestones in topological photonics and discuss how they can be built upon at the nanoscale.M.S.R. and S.J.P. would like to acknowledge their studentships from the Centre for Doctoral Training on Theory and Simulation of Materials at Imperial College London funded by EPSRC (Grant No. EP/L015579/1). S.R.P. acknowledges funding from EPSRC. X.X. is supported by a Lee family scholarship. P.A.H. acknowledges The Gordon and Betty Moore Foundation. V.G. acknowledges the Spanish Ministerio de Economia y Competitividad for financial support through the grant NANOTOPO (No. FIS2017-91413-EXP) and also Consejo Superior de Investigaciones Científicas (INTRAMURALES No. 201750I039). V.G. acknowledges support from CSIC Research Platform on Quantum Technologies PTI-001