One-dimensional Metallic Peanut-shaped Nanocarbon with Positive and Negative Gaussia Curvatures: Toward a New Science of Quantum Electronic Systems on Riemannian Surface

Abstract

When a C60 film is irradiated with a 3 kV electron-beam (EB) gun in vacuum (base pressure: 10−7 Pa), we have found that EB-irradiation of a C60 film gives rise to formation of a peanut-shaped C60 polymer with metallic electron-transport properties in air at room temperature. The peanut-shaped polymer has both positive and negative Gaussian curvatures (K), which can be classified into a new π-electron conjugated carbon allotrope that is different from graphite (K = 0), fullerenes (K > 0), nanotubes (K = 0 at body, K > 0 at cap edge), and hypothetical Mackay crystal (K < 0). In the present review article, we will introduce our recent results of the electron-transport, electronic, and optical properties of the nanocarbon, and describe theoretical analysis of its novel electronic properties on the basis of quantum mechanics on Riemannian surfaces. To our best knowledge, the peanut-shaped C60 polymer is only an existed material with a negative Gaussian curvature, whose electronic and optical properties are known experimentally. Thus we believe that the present system will open a new science “quantum science of condensed matters in Riemannian space”.