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

An exactly soluble model is used to study magnetization and persistent curr ents of electrons confined in two-dimensional mesoscopic rings and dots. Th e model allows the calculation of magnetization and persistent currents for a range of device geometries containing a large number of electrons (>10(3 )) with little computational requirement. It is shown that in the weak-magn etic-field limit, the persistent current is simply proportional to the magn etization, presenting Aharonov-Bohm (AB) type oscillations. Such oscillatio ns are aperiodic due to the penetration of magnetic field into the conducti ng region. In the strong-magnetic-held regime, however. the persistent curr ents and the magnetization have very different behaviors. While the persist ent currents still show a rapid AB-type oscillation, the magnetization is d ominated by de Haas-van Alphen (dHvA) type oscillations with the much weake r 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 a re very sensitive to the device geometry, while the magnetization in differ ent devices shows very similar dHvA-type oscillations. Our calculated typic al 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 4+/-2 nA. [S0163-1829(99)10331-X].