  Topological edge states exist at the interfaces between two
topologically-distinct materials. The presence and number of such modes are
deterministically predicted from the bulk-band topologies, known as the
bulk-edge correspondence. This principle is highly useful for predictably
controlling optical modes in resonators made of photonic crystals (PhCs),
leading to the recent demonstrations of micro-scale topological lasers.
Meanwhile, zero-dimensional topological trapped states in the nanoscale
remained unexplored, despite its importance for enhancing light-matter
interactions and for wide applications including single-mode nanolasers. Here,
we report a topological PhC nanocavity with a near-diffraction-limited mode
volume and its application to single-mode lasing. The topological origin of the
nanocavity, formed at the interface between two topologically-distinct PhCs,
guarantees the existence of only one mode within its photonic bandgap. The
observed lasing accompanies a high spontaneous emission coupling factor
stemming from the nanoscale confinement. These results encompass a way to
greatly downscale topological photonics.
