  We analyze a single-level quantum system placed between metallic leads and
strongly coupled to a localized vibrational mode, which models a singlemolecule
junction or an STM setup. We consider a polaron model describing the
interaction between electronic and vibronic degrees of freedom and develop and
examine different truncation schemes in the equation-of-motion method within
the framework of non-equilibrium Green functions. We show that upon applying
gate or bias voltage, it is possible to observe charge-bistability and
hysteretic behavior which can be the basis of a charge-memory element. We
further perform a systematic analysis of the bistability behaviour of the
system for different internal parameters such as the electron-vibron and the
lead-molecule coupling strength.
