Correlation effects of carbon nanotubes at boundaries: Spin polarization induced by zero-energy boundary states

When a carbon nanotube is truncated with certain type of edges, boundary states localized near the edges appear at the Fermi level. Starting from lattice models, low-energy effective theories are constructed which describe electron correlation effects on the boundary states. We then focus on a thin metallic carbon nanotube which supports one or two boundary states and discuss physical consequences of the interaction between the boundary states and bulk collective excitations. By the renormalization group analyses together with the open boundary bosonization, we show that the repulsive bulk interactions suppress the charge fluctuations at boundaries and assist the spin polarization.