  The experimental observation of quantum phenomena in mechanical degrees of
freedom is difficult, as the systems become linear towards low energies and the
quantum limit, and thus reside in the correspondence limit. Here we investigate
how to access quantum phenomena in flexural nanomechanical systems which are
strongly deflected by a voltage. Near a metastable point, one can achieve a
significant nonlinearity in the electromechanical potential at the scale of
zero point energy. The system could then escape from the metastable state via
macroscopic quantum tunneling (MQT). We consider two model systems suspended
atop a voltage gate, namely, a graphene sheet, and a carbon nanotube. We find
that the experimental demonstration of the phenomenon is currently possible but
demanding, since the MQT crossover temperatures fall in the milli-Kelvin range.
A carbon nanotube is suggested as the most promising system.
