Comment on 'Hysteresis, Switching, and Negative Differential Resistance in Molecular Junctions: a Polaron Model', by M. Galperin, M.A. Ratner, and A. Nitzan, Nano Lett. 5, 125 (2005)

It is shown that the ``hysteresis'' in a polaron model of electron transport through the molecule found by M.Galperin et al. [Nano Lett. 5, 125 (2005)] is an artefact of their ``mean-field'' approximation. The reason is trivial: after illegitimate replacement $\hat{n}^{2}=\hat{n}n_{0},$ where \hat{n} is the electron number operator, n_{0} the average molecular level occupation, Galperin et al. obtained non-physical dependence of a renormalized molecular energy level on the non-integer mean occupation number n_{0} (i.e. the electron self-interaction) and the resulting non-linearity of current. The exact theory of correlated polaronic transport through molecular quantum dots (MQDs) that we proposed earlier [Phys. Rev. B67, 235312 (2003)] proved that there is no hysteresis or switching in current-voltage characteristics of non-degenerate, d=1, or double degenerate, d=2, molecular bridges, contrary to the mean-field result. Switching could only appear in multiply degenerate MQDs with d>2 due to electron correlations. Most of the molecular quantum dots are in the regime of weak coupling to the electrodes addressed in our formalism.