Accessing topological synchronization in electrically driven semiconductor nano-laser arrays

We investigate topological synchronization in electrically driven semiconductor nanolaser arrays. By embedding a non-Hermitian topological Hamiltonian into complex-amplitude-carrier rate equations, we construct a nonlinear array model including carrier dynamics, linewidth enhancement, deterministic spontaneous emission, photon lifetime, and gain saturation. Numerical simulations show that when the coupling Hamiltonian is in a topological phase, edge nanolasers can form highly coherent frequency synchronization, whereas interior nanolasers do not participate in the same global locking process. A comparison with a trivial phase verifies that this selective edge synchronization originates from topological boundary modes rather than ordinary coupling-induced locking. Variations of parameters further show that the phenomenon is robust against changes in the Purcell factor and spontaneous-emission coupling factor but requires a finite window of pump strength and coupling strength. These results connect non-Hermitian topological photonics with realistic nanolaser-array dynamics and provide a theoretical route toward dense coherent nanolaser sources.