This chapter deals with the transport of charge carriers through carbon nanostructures in the presence of an external magnetic field, with emphasis on carbon nanotubes and on graphene. Specifically, we apply what was stated in Sections 4.4 and 5.4 about the interaction between these two types of nanomaterials with external magnetic fields, to the case of charge carrier transmission. As pointed out earlier, the presence of a magnetic field can have a significant impact on the electronic structure of a carbon nanosystem. Thus, the field may make a semiconducting nanotube metallic or turn a metallic tube into a semiconductor (see Sections 5.4.1 and 8.2). This observation suggests that magnetic fields might provide efficient tools to manipulate nanoelectronic circuits involving carbon elements. The present chapter explores this idea in the context of two fundamental phenomena that have been detected in carbon nanostructures, and subjected to detailed theoretical as well as experimental scrutiny, namely quantum magnetoresistance and the quantum Hall effect.

In Sections 11.1 to 11.3, we discuss the magnetoresistance of carbon nanotubes and of graphene, while the remainder of the chapter deals with the quantum Hall effect in graphene. Appreciating the basic results obtained in these two areas of topical research requires some familiarity with two key concepts of current condensed matter physics, namely Anderson localization and conductance in two-dimensional quantum Hall systems. This background information is provided in Sections 11.1 and 11.4. One might argue that the proper place for the final section of this chapter, 11.5.2, covering the quantum spin Hall effect, is in the previous chapter where spin transport phenomena are reviewed, for the twofold reason that the quantum spin Hall effect is about spin transmission, and that it does not involve any external magnetic field. While this objection is justified, the quantum spin Hall effect in graphene is included in the present chapter for facile comparison with other variants of the quantum Hall effect, as described in Sections 11.4 and 11.5.1.