Topological states of light have received significant attention due to the existence of counter-intuitive nontrivial boundary effects originating from the bulk properties of optical systems. Such boundary states, having their origin in topological properties of the bulk, are protected from perturbations and defects, and they show promises for a wide range of applications in photonic circuitry. The bulk-boundary correspondence relates the N-dimensional bulk modes to (N-1)-dimensional boundary states. Recently, the bulk-boundary correspondence was generalized to higher-order effects such that an N-dimensional bulk defines its (N-M)-dimensional boundary states. Prominent examples are topological corner states of light in two-dimensional structures that have been realized at the micrometer-scale. Such corner states, due to their tight confinement in all directions, provide a novel route towards topological cavities. Here we bring the concept of topological corner states to the nanoscale for enhancing nonlinear optical processes. Specifically, we design topologically nontrivial hybrid metasurfaces with C6-symmetric honeycomb lattices supporting both edge and corner states. We report on direct observations of nanoscale topology-empowered localization of light in corner states revealed via a nonlinear imaging technique. Nanoscale topological corner states pave the way towards on-chip applications in compact classical and quantum nanophotonic devices.
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