Magnetic quantum dots and magnetic edge states

Starting with defining the magnetic edge state in a magnetic quantum dot, which becomes quite popular nowadays conjunction with a possible candidate for a high density memory device or spintronic materials, various magnetic nano-quantum structures are reviewed in detail. We study the magnetic edge states of the two dimensional electron gas in strong perpendicular magnetic fields. We find that magnetic edge states are formed along the boundary of the magnetic dot, which is formed by a nonuniform distribution of magnetic fields. These magnetic edge states circulate either clockwise or counterclockwise, depending on the number of missing flux quanta, and exhibit quite different properties, as compared to the conventional ones which are induced by electrostatic confinements in the quantum Hall system. We also find that a close relation between the quantum mechanical eigenstates and the classical trajectories in the magnetic dot. When a magnetic dot is located inside a quantum wire, the edge-channel scattering mechanism by the magnetic quantum dot is very different from that by electrostatic dots. Here, the magnetic dot is formed by two different magnetic fields inside and outside the dot. We study the ballistic edge-channel transport and magnetic edge states in this situation. When the inner field is parallel to the outer one, the two-terminal conductance is quantized and shows the features of a transmission barrier and a resonator. On the other hand, when the inner field-is reversed, the conductance is not quantized and all channels can be completely reflected in some energy ranges. The difference between the above two cases results from the distinct magnetic confinements. We also describe successfully the edge states of magnetic quantum rings and others in detail. (C) 2003 Elsevier B.V. All rights reserved.