Novel Electronic Properties of a Graphene Antidot, Parabolic Dot, and Armchair Ribbon

Authored by: S.R. Eric Yang , S. C. Kim

Graphene Science Handbook

Print publication date:  April  2016
Online publication date:  April  2016

Print ISBN: 9781466591318
eBook ISBN: 9781466591325
Adobe ISBN:

10.1201/b19642-15

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Abstract

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 Landau levels. In this regime, wavefunctions become anomalous with a narrow probability density peak inside the barrier and another broad peak outside the potential barrier with the width comparable to the magnetic length. The second example is a graphene parabolic dot in the presence of a magnetic field. One counterintuitively finds that resonant quasi-bound states of both positive and negative energies exist in the energy spectrum. The presence of resonant quasi-bound states of negative energies is a unique property of massless Dirac fermions. Also, when the strength of the potential increases, resonant and nonresonant states transform into discrete anomalous states with a narrow probability density peak inside the well and another broad peak under the potential barrier with the width comparable to the magnetic length. The 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 = 3Ma 0, depending on the value of the Fermi energy, a ferromagnetic or paramagnetic state can be stable while for L x = (3M + 1)a 0, the paramagnetic state is stable (M is an integer and a 0 is the length of the unit cell). Ferromagnetic and paramagnetic states are well suited for spintronic applications.

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