  We investigate the current noise of nanoelectromechanical systems close to a
continuous mechanical instability. In the vicinity of the latter, the
vibrational frequency of the nanomechanical system vanishes, rendering the
system very sensitive to charge fluctuations and, hence, resulting in very
large (super-Poissonian) current noise. Specifically, we consider a suspended
single-electron transistor close to the Euler buckling instability. We show
that such a system exhibits an exponential enhancement of the current noise
when approaching the Euler instability which we explain in terms of telegraph
noise.
