We report the production and characterization of a form of amorphous carbon films with sp/sp2 hybridization (atomic fraction of sp hybridized species > 20%) where the predominant sp bonding appears to be (=C=C=)n cumulene. Vibrational and electronic properties have been studied by in situ Raman spectroscopy and electrical conductivity measurements. Cumulenic chains are substantially stable for temperatures lower than 250 K and they influence the electrical transport properties of the sp/sp2 carbon through a self-doping mechanism by pinning the Fermi level closer to one of the mobility gap edges. Upon heating above 250 K the cumulenic species decay to form graphitic nanodomains embedded in the sp2 amorphous matrix thus reducing the activation energy of the material. This is the first example of a pure carbon system where the sp hybridization influences bulk properties.