Novel electronic properties of a graphene antidot, parabolic dot, and armchair ribbon

Graphene nanostructures have great potential for device applications. However, they can exhibit several counterintuitive electronic properties not present in ordinary semiconductor nanostructures. In this chapter, we review several of these graphene nanostructures. A first example is a graphene antidot that possesses boundstates inside the antidot potential in the presence of a magnetic field. As the range of the repulsive potential decreases in comparison to the magnetic length, the effective coupling constant between the potential and electrons becomes more repulsive, and then, it changes the sign and becomes attractive. This is a consequence of a subtle interplay between Klein tunneling and quantization of last example is a one-dimensional electron gas in the lowest energy conduction subband of graphene armchair ribbons. Bulk magnetic properties of it may sensitively depend on the width of the ribbon. For ribbon widths L_x = 3Ma₀, depending on the value of the Fermi energy, a ferromagnetic or paramagnetic state can be stable while for L_x = (3M + 1)a₀, the paramagnetic state is stable (M is an integer and a0 is the length of the unit cell). Ferromagnetic and paramagnetic states are well suited for spintronic applications.