Period doubling effects in the oscillations of persistent currents in discretized Aharonov–Bohm rings

One shows that the oscillations with respect to the magnetic flux in the one-dimensional discretized Aharonov–Bohm rings are sensitive with respect to the parity of the number of electrons Ne. Resorting to basic flux intervals of unit length indicates that the period of such oscillations is given by the flux quantum Φ0=hc/e and by 2Φ0 if Ne is odd and even, respectively. Accordingly, one deals with a period doubling effect when passing from odd Ne-values to even ones, which may be useful in the design of further nanodevices. Interaction free limits of the Drude weight are also discussed.