  Theory of current hysteresis for tunneling through a molecular quantum dot
(MQD) with strong electron-vibron interactions and attractive electron-electron
correlations is developed. The dot is modeled as a d-fold degenerate energy
level weakly coupled to the leads. The effective attractive interaction between
polarons in the dot results in a "switching" phenomenon in the current-voltage
characteristics when d>2, in agreement with the results for the
phenomenological negative-U model. The degenerate MQD with strong
electron-vibron coupling has two stable current states in certain interval of
the bias voltage below some critical temperature.
