Theory of scanning tunneling spectroscopy of fullerene peapods

A theory for the hybridization of tube and encapsulant derived electronic states is developed for fullerene peapods: carbon nanotubes encapsulating molecular ${\mathrm{C}}_{60}.$ The interaction between tube and encapsulant is constrained by symmetry and it is studied using a long-wavelength theory of the tube states and a nearly free particle theory of the ball orbitals. Calculations of the local densities of states, resolved in energy and position, are obtained for the gapped bands of a nanotube interacting with a single encapsulated fullerene, with an encapsulated dimer, and with a periodic fullerene peapod lattice. The calculations identify features in the bound state and scattering spectra of the tube produced by hybridization with the encapsulant. For the peapod lattice we identify (a) a narrow defect induced electronic band, (b) a hybridization gap resulting from the strong mixing of tube and ball degrees of freedom, and (c) Bragg gaps produced by electron motion in a periodic defect potential. The theory provides a good description of the prominent features of the measured electronic spectra of fullerene peapods obtained by low-temperature scanning tunneling microscopy.