Persistent currents in one-dimensional aperiodic mesoscopic rings

In the tight-binding approximation, we have investigated the behaviour of persistent currents in a one-dimensional Thue-Morse mesoscopic ring threaded by a magnetic flux. By applying a transfer-matrix technique, the energy spectra and the persistent currents in the system have been numerically calculated. It is shown that the flux-dependent eigenenergies form “band” structures and the energy gaps will enlarge if the site energy increases. Actually, the site energy and the filling-up number of electrons are two important factors which have much influence upon the persistent current. Increment of the site energy in the system will lead to a dramatic suppression of the currents. When the highest-occupied energy level is on the top of the band, the total current is limited; otherwise, the persistent current increases by several orders of magnitude. Generally, this kind of large scale change in the magnitude of the current can easily be observed in the vicinity of band gaps. The parity effect in the Thue-Morse ring is also discussed. Received 22 January 2001 and Received in final form 25 October 2001