Persistent currents as an indication of localization in energy space.

Abstract

We show theoretically that localization in energy space is reflected in an experimentally accessible quantity: persistent currents in mesoscopic systems. We study the persistent current J(t)=${\mathit{J}}_{\mathit{d}\mathit{c}}$+${\mathit{J}}_{\mathit{a}\mathit{c}}$(t) in a normal mesoscopic ring or cylinder, induced by a time-dependent Aharonov-Bohm magnetic flux \ensuremath{\varphi}(t)=${\mathrm{\ensuremath{\varphi}}}_{\mathit{d}\mathit{c}}$+${\mathrm{\ensuremath{\varphi}}}_{\mathit{a}\mathit{c}}$sin(wt), where w is very large. It is shown that for general values of ${\mathrm{\ensuremath{\varphi}}}_{\mathit{a}\mathit{c}}$, ${\mathit{J}}_{\mathit{d}\mathit{c}}$ is of the same (finite) order of magnitude as the persistent current carried by a single level. ${\mathit{J}}_{\mathit{a}\mathit{c}}$(t) is very small, and in its Fourier spectrum there is a significant contribution from only a small number of frequencies, clustered near a lower cutoff frequency. For special values of ${\mathrm{\ensuremath{\varphi}}}_{\mathit{a}\mathit{c}}$, ${\mathit{J}}_{\mathit{d}\mathit{c}}$ sharply drops to nearly zero, while ${\mathit{J}}_{\mathit{a}\mathit{c}}$(t) increases. Arbitrarily small frequencies appear in the Fourier spectrum of ${\mathit{J}}_{\mathit{a}\mathit{c}}$(t), which contains a larger number of frequencies. This behavior is explained as a manifestation of localization in energy-space effects, and can be used as a method to detect this localization. The method is applicable even in the presence of a sufficiently large finite inelastic relaxation time.