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Theory of current hysteresis for tunneling through a molecular quantum dot(MQD) with strong electron-vibron interactions and attractive electron-electroncorrelations is developed. The dot is modeled as a d-fold degenerate energylevel weakly coupled to the leads. The effective attractive interaction betweenpolarons in the dot results in a "switching" phenomenon in the current-voltagecharacteristics when d>2, in agreement with the results for thephenomenological negative-U model. The degenerate MQD with strongelectron-vibron coupling has two stable current states in certain interval ofthe bias voltage below some critical temperature.Comment: 8 pages, 4 figure

Memory effect in a molecular quantum dot with strong electron-vibron interaction