  We study the transport properties of an Anderson-Holstein model with orbital
degeneracies and a tunneling phase that allows for the formation of dark
states. The resulting destructive interference yields a characteristic pattern
of positive and negative differential conductance features with enhanced shot
noise, without further asymmetry requirements in the coupling to the leads. The
transport characteristics are strongly influenced by the Lamb-shift
renormalization of the system Hamiltonian. Thus, the electron-vibron coupling
cannot be extracted by a simple fit of the current steps to a Poisson
distribution. For strong vibronic relaxation, a simpler effective model with
analytical solution allows for a better understanding and moreover demonstrates
the robustness of the described effects.
