  Strong coupling of electronic and vibrational degrees of freedom entails a
low-bias suppression of the current through single-molecule devices, termed
Franck-Condon blockade. In the limit of slow vibrational relaxation, transport
in the Franck-Condon-blockade regime proceeds via avalanches of large numbers
of electrons, which are interrupted by long waiting times without electron
transfer. The avalanches consist of smaller avalanches, leading to a
self-similar hierarchy which terminates once the number of transferred
electrons per avalanche becomes of the order of unity. Experimental signatures
of self-similar avalanche transport are strongly enhanced current (shot) noise,
as expressed by giant Fano factors, and a power-law noise spectrum. We develop
a theory of the Franck-Condon-blockade regime with particular emphasis on
effects of electron cotunneling through highly excited vibrational states. As
opposed to the exponential suppression of sequential tunneling rates for
low-lying vibrational states, cotunneling rates suffer only a power-law
suppression. This leads to a regime where cotunneling dominates the current for
any gate voltage. Including cotunneling within a rate-equation approach to
transport, we find that both the Franck-Condon blockade and self-similar
avalanche transport remain intact in this regime. We predict that cotunneling
leads to absorption-induced vibrational sidebands in the Coulomb-blockaded
regime as well as intrinsic telegraph noise near the charge degeneracy point.
