Quantum behavior in one-dimensional mesoscopic Thue-Morse rings

Using a tight-binding model, we have investigated the energy spectra and persistent currents in one-dimensional mesoscopic rings threaded with a magnetic flux phi. The mesoscopic ring is constructed by a Thue-Morse chain with N sites. By applying a transfer-matrix method, the flux-dependent energy spectra have been obtained. It is shown that the electron eigenenergies E(phi) gradually form "bands" as the disorder increases in the quantum system. Meanwhile, the persistent currents in the rings exhibit a rich structure, which depends on the number of electrons and the disorder of system. On the other hand, as increasing the disorder of system, the "bandwidths" are getting narrower in the energy spectra; thereafter the maximum persistent current decreases obviously in the rings. A metal-insulator transition can be easily found in the half-filled electron system.