The electronic spectrum of a two-dimensional square lattice in a perpendicular magnetic field has become known as the Hofstadter butterfly [Hofstadter, Phys. Rev. B 14, 2239 (1976)]. We have calculated quasi-one-dimensional analogs of the Hofstadter butterfly for carbon nanotubes (CNTs) and graphene. Single-wall CNTs and graphene nanoribbons in perpendicular magnetic fields show a rich, pseudofractal spectrum, that can be related to the butterfly of planar graphene. In double-wall CNTs, the interlayer interaction adds modulations in the spectrum that can be understood by studying the effects of intense magnetic fields onto bilayer graphene which is per se an interesting material due to its anomalous quantum Hall effect that could recently be measured in experiment.
The electronic spectrum of a two-dimensional square lattice in a perpendicular magnetic field has become known as the Hofstadter butterfly [Hofstadter, Phys. Rev. B 14, 2239 (1976)]. We have calculated quasi-one-dimensional analogs of the Hofstadter butterfly for carbon nanotubes (CNTs) and graphene. Single-wall CNTs and graphene nanoribbons in perpendicular magnetic fields show a rich, pseudofractal spectrum, that can be related to the butterfly of planar graphene. In double-wall CNTs, the interlayer interaction adds modulations in the spectrum that can be understood by studying the effects of intense magnetic fields onto bilayer graphene which is per se an interesting material due to its anomalous quantum Hall effect that could recently be measured in experiment.
