Persistent currents in mesoscopic rings : ensemble averages and half-flux-quantum periodicity

An isolated metallic loop, whose dimensions are smaller than the electronic phase coherence length, is expected to present a permanent current in the presence of a magnetic field through the loop. For a single ring, it has been shown that this permanent current (which is a consequence of the sensitivity of the energy levels to the change of boundary conditions determined by the magnetic field) is a periodic function of the magnetic flux Φ with a period Φ0 = h/e. We are interested here in the magnetic moment of an assembly of independent multichannel rings. We show that this ensemble average is periodic in Φ0/2. On findings rely on both analytical arguments and numerical simulations on the Anderson model. In the zero disorder limit, the ensemble average is independent of the number of channels. In the strong disorder limit, /I0 is of the order of the square of the typical current /I20 (expressed in I0 = evF/L units). We emphasize the fact that these results are obtained with a fixed number of electrons in each ring (this number being different from one ring to the other). Calculations performed when fixing the chemical potential do not yield this Φ 0/2 periodicity.