Ultra-compact III-V nanolasers monolithically integrated on Si with ultra-low energy consumption and small modal volume have been emerged as one of the most promising candidates to achieve Si on-chip light sources. However, the significant material dissimilarities between III-V and Si fundamentally limit the performance of Si-based III-V nanolasers. In this work, we report 1.3 μm InAs/GaAs quantum-dot photonic-crystal (PhC) nanobeam lasers directly grown on complementary metal-oxide-semiconductor compatible on-axis Si (001) substrates. The continuous-wave optically pumped PhC nanobeam lasers exhibited a single-mode operation, with an ultra-low lasing threshold of ∼ 0.8 μW at room temperature. In addition, a nanoscale physical volume of ∼ 8 × 0.53 × 0.36 μm ³ (∼ 25 (λ n ⁻¹ ) ³ ) was realized through a small number of air-holes in PhC nanobeam laser. The promising characteristics of the PhC nanobeam lasers with small footprint and ultra-low energy consumption show their advanced potential towards densely integrated Si photonic integrated circuits.

Large winding number as the unique characteristics of topological phenomena has been garnering widespread interest owing to its rich physics and potential applications in enhanced information capacity. In this work, we report the realization of the large winding number and multifold topological phase transitions by introducing layer degrees of freedom to construct topological heterostructures and experimentally demonstrate the topological edge states for circuit heterostructures in the circuit system. The effective decomposition of circuit heterostructures into independent subspaces is revealed. The multiple topological phase transitions and different large winding numbers for heterostructures can be triggered by tuning the topological properties of the subspace, leading to the multiple topological edge states reflecting in finite-size systems. Our work provides an intuitive and universal way to access the tunable large winding number and multifold topological phase transitions and may apply to engineering unique topological phenomena and further applications in classical wave systems.