Giant persistent currents in quasiperiodic mesoscopic rings

•Giant persistent currents occurring in quasiperiodic mesoscopic rings are proposed.•The maximum persistent current increases exponentially with the system order.•The maximum persistent current occurs on transport resonances.•The persistent current is proportional to sharpness of the transport resonance.

Giant persistent currents that occur in quasiperiodic Thue–Morse array of mesoscopic rings are proposed. As the order of the system increases, the maximum persistent current increases exponentially. The giant persistent current in a system with higher order is greater than that in traditional structures. It is found that the maximum persistent current occurs in the ring near the middle position of the array. The persistent current is also proportional to the sharpness of the transport resonance, which is dependent on the width of the allowed band in the bandstructure. A rule to determine the occurrence energy of the giant persistent currents for a system with arbitrary order is also proposed.