  Considering irreducibility is fundamental for studying the ergodicity of
stochastic dynamical systems. In this paper, we establish the irreducibility of
stochastic complex Ginzburg-Laudau equations driven by pure jump noise. Our
results are dimension free and the conditions placed on the driving noises are
very mild. A crucial role is played by criteria developed by the authors of
this paper and T. Zhang for the irreducibility of stochastic equations driven
by pure jump noise. As an application, we obtain the ergodicity of stochastic
complex Ginzburg-Laudau equations. We remark that our ergodicity result covers
the weakly dissipative case with pure jump degenerate noise.
