Electronic spectrum and tunneling properties of multiwall carbon nanotubes

We develop a general approach to calculations of the electron spectrum of metallic multiwall carbon nanotubes (MWNTs) with an arbitrary number of coaxial layers. It is based on the model with singular attractive potential of equidistant conductive cylinders. The knowledge of the one-electron spectrum allows us to construct the corresponding Green function and then to calculate the entropy and density of states for the MWNT. We analyze the tunneling between the nanotube and normal metal electrode. The possibility of the direct determination of the one-electron density of states by measurements of the tunneling conductivity at low temperatures is proved and the necessary restrictions on temperature are formulated. We discuss briefly the conflicting experimental observations of electronic properties of a MWNT.