Scanning Tunneling Microscopy and Spectroscopy have been used in an attempt to elucidate the electronic structure of nanotube systems containing two constituent shells. Evidence for modified electronic structure due to the inter-layer interaction in double-walled carbon nanotubes is provided by the experimental tunneling spectra and the contribution of the inner tube to the local density of states of the "composite" double-walled system is identified in agreement with previous theoretical calculations. An explicit correlation between the chirality of the two constituent tubes, the inter-wall interaction and the overall electronic structure for double-walled carbon nanotubes, is demonstrated by our experiments, showing that the effect the inner tube has on the overall electronic structure of double-walled nanotubes cannot be neglected, and is key to the opto-electronic properties of the system. We postulate that previous analysis of the opto-electronic properties on multiple-walled carbon nanotubes based purely on the outer layer chirality of the tube needs significant modification based on new understanding brought forth with our analysis.
