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Chapter 4. Conclusion
In this dissertation, we have addressed the topics of persistent charge current and spin current in one-dimensional mesoscopic rings.
In chapter one, we focus on the persistent charge current in normal metal rings without spin degree of freedom. From the magnetic response of mesoscopic copper rings measured by Lévy et al. [15], we learn that persistent charge currents really exist in normal metal rings. The period of the oscillation current is independent of the frequency of the time-varying flux and corresponds to a half-flux-quantum because of the large number of loops in the ring.
From the magnetic response of a single mesosize of gold ring measured by Chandrasekhar et al. [16], we learn that the period of the persistent charge current of the single ring corresponds to one flux quantum. Besides, the magnitudes of the persistent charge currents are a factor of 30 to 150 times larger than the theoretical estimates.
In chapter two, we focus on spin-orbit coupling in two-dimensional system with both charge and spin degrees of freedom. From the theoretical discussion of the behavior of mesoscopic isolated semiconductor rings with RSO coupling given by Lozano [28] and us, we learn that the structure of energy levels for the ring is an analogy of the band structure for Bloch electrons. The effect of RSO coupling is to lower the energy states and change the order of fundamental states. Besides, the distribution of the total spin density along the radial direction exhibits spin accumulation at the borders of the ring in the presence of magnetic flux and RSO coupling without external electric field.
In chapter three, we focus on the persistent spin current in insulator magnetic rings without charge degree of freedom. From the theoretical discussion of the behavior of ferromagnetic spin rings subject to a nonuniform magnetic field given by Schütz et al. [25], we learn that the persistent spin current will exist in such a ring. The persistent spin current is found to be zero at temperature T=0 and proportional to T at finite temperature.
For antiferromagnetic spin rings subject to a nonuniform magnetic field given by Schütz et al. [55], the persistent spin current in such an antiferromagnetic spin ring can be nonzero at temperature T=0 due to quantum fluctuations. Besides, the magnitude of the spin current exhibits sawtooth characteristics with respect to geometric phase, similar to the behavior of persistent charge current in a metal ring.
For ferrimagnetic spin rings subject to a nonuniform magnetic field [46], the ferrimagnetic spin ring can have either ferromagnetic or antiferromagnetic characteristics. A nonzero persistent spin current exists at temperature T=0, similar to the case of the antiferromagnetic spin ring. On the other hand, the magnitude of the persistent spin current is proportional to temperature T, similar to the case of ferromagnetic spin ring.
