Localized cap states are discussed in caps consisting of q graphene sheets of regular triangles (1 ≤ q ≤6) attached to a metallic nanotube both analytically and numerically in an effective-mass approximation. There are cap states at ε = 0 (the energy of a carbon π-orbital) associated with first excited conduction band and highest valence band. Cap states associated with other bands lie in the vicinity of the corresponding band edges. The wave function behaves as r -1/5 in the vicinity of a five-membered ring for states with ε = 0, where r is the distance from the ring.
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Yaguchi et al. (2002) studied this question.
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