Fano Resonance and Orbital Filtering in Multiply Connected Carbon Nanotubes

We investigate the electron transport in multiply connected metallic carbon nanotubes within the Landauer-B\"{u}ttiker formalism. Quasibound states coupled to the incident $\pi^{*}$ states give rise to energy levels of different widths depending on the coupling strength. In particular, donorlike states originating from heptagonal rings are found to give a very narrow level. Interference between broad and narrow levels produces Fano-type resonant backscattering as well as resonant tunneling. Over a significantly wide energy range, almost perfect suppression of the conduction of $\pi^{*}$ electrons occurs, which may be regarded as filtering of particular electrons ($\pi$-pass filter).