Magnetization, persistent currents, and their relation in quantum rings and dots

Abstract

An exactly soluble model is used to study magnetization and persistent currents of electrons confined in two-dimensional mesoscopic rings and dots. The model allows the calculation of magnetization and persistent currents for a range of device geometries containing a large number of electrons $(g{10}^{3})$ with little computational requirement. It is shown that in the weak-magnetic-field limit, the persistent current is simply proportional to the magnetization, presenting Aharonov-Bohm (AB) type oscillations. Such oscillations are aperiodic due to the penetration of magnetic field into the conducting region. In the strong-magnetic-field regime, however, the persistent currents and the magnetization have very different behaviors. While the persistent currents still show a rapid AB-type oscillation, the magnetization is dominated by de Haas--van Alphen (dHvA) type oscillations with the much weaker AB-type oscillations superimposed on them. The effect of device geometry on the persistent current is also very different from that on magnetization. Both the oscillation amplitude and the period of the persistent current are very sensitive to the device geometry, while the magnetization in different devices shows very similar dHvA-type oscillations. Our calculated typical value of weak-magnetic-field persistent current in a semiconductor ring, 4.95 nA, is in very good agreement with the experimental result of Mailly, Chapelier, and Benoit [Phys. Rev. Lett. 70, 2020 (1993)]: $4\ifmmode\pm\else\textpm\fi{}2$ nA.