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We study the electronic structure of the junctions between a single graphenelayer and carbon nanotubes, using a tight-binding model and the continuumtheory based on Dirac fermion fields. The latter provides a unified descriptionof different lattice structures with curvature, which is always localized atsix heptagonal carbon rings around each junction. When these are evenly spaced,we find that it is possible to curve the planar lattice into armchair (6n,6n)as well as zig-zag (6n,0) nanotubes. We show that the junctions fall into twodifferent classes, regarding the low-energy electronic behavior. One of them,constituted by the junctions made of the armchair nanotubes and the zig-zag(6n,0) geometries when n is a multiple of 3, is characterized by the presenceof two quasi-bound states at the Fermi level, which are absent for the rest ofthe zig-zag nanotubes. These states, localized at the junction, are shown toarise from the effective gauge flux induced by the heptagonal carbon rings,which has a direct reflection in the local density of states around thejunction. Furthermore, we also analyze the band structure of the arrays ofjunctions, finding out that they can also be classified into two differentgroups according to the low-energy behavior. In this regard, the arrays made ofarmchair and (6n,0) nanotubes with n equal to a multiple of 3 are characterizedby the presence of a series of flat bands, whose number grows with the lengthof the nanotubes. We show that such flat bands have their origin in theformation of states confined to the nanotubes in the array. This is explainedin the continuum theory from the possibility of forming standing waves in thementioned nanotube geometries, as a superposition of modes with oppositemomenta and the same quantum numbers under the C_6v symmetry of the junction.

Propagating, evanescent, and localized states in carbon nanotube-graphene junctions