Electronic spectrum and tunnelling properties of multi-wall carbon nanotubes

We develop a general approach to calculations of the electron spectrum of metallic multi-wall carbon nanotubes (MWNT) with arbitrary number of coaxial layers. It is based on the model with singular attractive potential of equidistant conductive cylinders. The knowledge of one-electron spectrum allows to construct the corresponding Green function and then to calculate the entropy and density of states for MWNT. We analyze the tunnelling between the nanotube and normal metal electrode. The possibility of direct determination of one-electron density of states by measurements of the tunnelling 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 MWNT.