Abstract
Polaron theory of 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 a certain interval of the bias voltage below some critical temperature.
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