Electromechanical instability in vibrating quantum dots with effectively negative charging energy

In quantum dots or molecules with vibrational degrees of freedom the electron-vibron coupling renormalizes the electronic charging energy. For sufficiently strong coupling, the renormalized charging energy can become negative. Here, we discuss an instability towards adding or removing an arbitrary number of electrons when the magnitude of the renormalized charging energy exceeds the single-particle level spacing. We show that the instability is regularized by the anharmonic contribution to the vibron energy. The resulting effective charging energy as a function of the electron number has a double-well structure causing a variety of novel features in the Coulomb blockade properties.