On the Typical and Average Contributions to the Persistent Current in Mesoscopic Rings

Abstract

Low-temperature measurements of the magnetic response of one or more electrically-isolated, micron-sized metallic rings yield an unexpected yet unequivocal result: the presence of equilibrium <i>persistent</i> currents, with nanoampere-sized amplitudes and either <i>h/e</i>- or <i>h/2e</i>-periodicity in the applied magnetic flux. This effect follows from the extended phase coherence of the conduction electrons in this disordered mesoscopic system. As with transport phenomena, this thermodynamic effect demonstrates sample-specific as well as ensemble-averaging qualities common to mesoscopic physics. With few exceptions, however, there is strong disagreement between the different theoretical calculations and the few successful experiments to date.

For this thesis work, we have designed and executed a unique and unprecedented new experiment: the measurement of the sign, amplitude, and temperature dependences of both the typical and average current contributions to the <i>h/e</i>- and <i>h/2e</i>-periodic magnetic response of the same sample of thirty mesoscopic Au rings. Of particular interest here is the innovative design of our custom SQUID-based detector as well as the unusually long phase coherence of electrons in our lithographically-patterned Au sample. Remarkably, both the typical and average contributions are diamagnetic in sign near zero field, over multiple cooldowns, and comparable in magnitude per ring to the Thouless scale E_c of energy level correlations. Taken in conjunction with earlier experiments, the new data strongly challenge conventional theories of the persistent current.