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 n^2=n^n0, 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.Comment: 3 pages, no figures; (v3) estimates added showing that most of the
molecules are very resistive, so the actual molecular quantum dots are in the
regime we study, unlike very transparent `molecules' studied by Galperin et
al and other authors. In the latter case the molecules are rather
`transparent' and, obviously, no current hysteresis can exis