Title: Electrically pumped topological laser with valley edge modes

Abstract: Quantum cascade lasers are compact, electrically pumped light sources in the technologically important mid-infrared and terahertz region of the electromagnetic spectrum. Recently, the concept of topology has been expanded from condensed matter physics into photonics, giving rise to a new type of lasing using topologically protected photonic modes that can efficiently bypass corners and defects. Previous demonstrations of topological lasers have required an external laser source for optical pumping and have operated in the conventional optical frequency regime. Here we demonstrate an electrically pumped terahertz quantum cascade laser based on topologically protected valley edge states. Unlike topological lasers that rely on large-scale features to impart topological protection, our compact design makes use of the valley degree of freedom in photonic crystals, analogous to two-dimensional gapped valleytronic materials. Lasing with regularly spaced emission peaks occurs in a sharp-cornered triangular cavity, even if perturbations are introduced into the underlying structure, owing to the existence of topologically protected valley edge states that circulate around the cavity without experiencing localization. We probe the properties of the topological lasing modes by adding different outcouplers to the topological cavity. The laser based on valley edge states may open routes to the practical use of topological protection in electrically driven laser sources.