  Nonlinear topological photonic and phononic systems have recently aroused
intense interests in exploring new phenomena that have no counterparts in
electronic systems. The squeezed bosonic interaction in these systems is
particularly interesting, because it can modify the vacuum fluctuations of
topological states, drive them into instabilities, and lead to topological
parametric lasers. However, these phenomena remain experimentally elusive
because of limited nonlinearities in most existing topological bosonic systems.
Here, we experimentally realized topological parametric lasers based on
nonlinear nanoelectromechanical Dirac-vortex cavities with strong squeezed
interaction. Specifically, we parametrically drove the Dirac-vortex cavities to
provide phase-sensitive amplification for topological phonons, and observed
phonon lasing above the threshold. Additionally, we confirmed that the lasing
frequency is robust against fabrication disorders and that the free spectral
range defies the universal inverse scaling law with increased cavity size,
which benefit the realization of large-area single-mode lasers. Our results
represent an important advance in experimental investigations of topological
physics with large bosonic nonlinearities and parametric gain.
