A degeneracy is lifted, and the bandgap opens by dimerization between the first and second bands in the vicinity of the K point. The inset shows the unit cell and dimensions of the structure: lattice period aвЂ‰=вЂ‰460вЂ‰nm, sizes of triangulated holes r 1вЂ‰=вЂ‰174вЂ‰nm, r 2вЂ‰=вЂ‰269вЂ‰nm, and slab thickness fixed to 250вЂ‰nm. The grey shaded regions indicate the light cone. d Numerically calculated bulk photonic band structure for TE-like modes. b, c Tight-binding model visualization of optical modes of the structure. The shaded yellow stripe illustrates a supercell with a zigzag cut. The structure is implemented in a dielectric photonic crystal slab of a finite thickness.

While lasing in the first nanoscale topological systems has been associated with cryogenic temperatures 5, 6, 10, we reach the lasing regime at room temperature.ДЄ A closed domain wall is created by inversion symmetry breaking in the dimerized graphene lattice and shaped in the form of an equilateral triangle (reddish area). We demonstrate low-threshold lasing under uniform pumping from high-quality cavity modes hosted within the topological bandgap of the structure. The structures include IIIвЂ“V semiconductor quantum wells that act as a gain medium and serve as an internal light probe in the near infrared region. Here, we study lasing from valley-Hall nanophotonic cavities embedded into 2D topological lattices 15, 16, 21. Harnessing topological phases and hyperuniformity 20 in photonic nanostructures opens new horizons in designing advanced integrated nanoscale light sources with controllable properties. Pulsed optical pumping at powers relatively close to the lasing threshold assumes that observations can be largely explained in terms of the physics of linear modes. The general exciting motivation of those studies is that the concepts of topology may serve as a significant guiding scheme for the smart control of the number, spectral separation, localization scales and quality factors of edge and defect modes in topological cavities for lasing. Most recently, a band-inversion mechanism was used to implement lasing in a bulk state trapped by a two-dimensional (2D) hexagonal cavity in a KekulГ©-patterned InGaAsP slab 19. 11 demonstrated lasing driven by midgap edge states in a dimer chain of nanocavities arranged in a hexagonal InAsP/InP multiple-quantum-well photonic crystal. 10 reported single-mode lasing from topological defect modes created in a patterned nanobeam GaAs photonic crystal with embedded InAs quantum dots. In this direction, two recent pioneering studies employed photonic structures emulating a one-dimensional (1D) SuвЂ“SchriefferвЂ“Heeger model 10, 11. High-index dielectrics such as IIIвЂ“V semiconductors can be designed to contain strong optical gain further enhanced by topological field localization, forming a favourable platform for active topological nanophotonics 10, 11, 19. Nanostructures made of high-index dielectric materials with judiciously designed resonant elements and lattice arrangements show special promise for the practical implementation of topological order for light. Motivated by optical on-chip applications, special efforts have been made toward bringing topological photonics to the nanoscale 13, 14, 15, 16, 17, 18. Above the lasing threshold, it also becomes crucial to account for gain saturation and other nonlinear effects, such as Kerr self-action, that pose interesting new challenges in bridging topological photonics with nonlinear optics 12. Recent experimental demonstrations include single-mode lasing based on a topologically protected edge state in micro-resonator arrays 8 and unidirectional outcoupling of laser emission from magnetic-field biased photonic crystal cavities of arbitrary shapes 6. The synergy between non-Hermiticity and topology in active optical systems offers both new physics governed by non-Hermitian Hamiltonians 3, 4 and potential applications for the design of topological lasers with superior characteristics and tolerance to fabrication imperfections 5, 6, 7, 8, 9, 10, 11. In this scope, topologically robust wave transport typically relies on symmetry-protected edge states supported by interfaces between domains characterized by distinct topological invariants 2. Topological phases of light provide unique opportunities to create photonic systems immune to scattering losses and disorder 1.

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