Nearly free electron states in carbon nanotube bundles

On the basis of density-functional theory, we study electronic structures of thin carbon nanotube bundles. We find that nearly-free-electron (NFE) states, which are distributed in intra- and intertube regions, are present at $3\sim 4\mathrm{eV}$ above the Fermi level. In the intertube region the NFE state of the nanotube bundles are strongly modified from that of the isolated nanotube. We also find that mixing of the NFE state with ${\mathrm{sp}}^2$ orbitals at atomic sites is decisive in a peculiar behavior of their charge distribution. Importance of the NFE state in transport properties is discussed.