Geometric boundary effects on the electronic properties of finite carbon nanotubes

Quantum finite-size effects in carbon nanotubes are studied as a function of tube length L and of the type of end structure used to terminate the tube. The "end" structures considered are: tori, open tubes terminated with H atoms, and various caps formed from hemispherical pieces of fullerenes. With different geometric boundaries there arise distinct asymptotic band-gap behaviors as a function of L: damped oscillations decaying as 1/L, monotonic 1/L decay, exponentially decaying, and constant. These asymptotic scaling behaviors are categorized and explained in terms of general characteristics of the frontier orbitals. Implications for nanoscale devices are briefly discussed. (C) 1997 Elsevier Science Ltd.