THE EFFECT OF DISORDER IN SMALL ONE-DIMENSIONAL NORMAL-METAL RINGS

The effect of disorder on the state of the electron in mesoscopic-one- dimensional normal metal rings is considered. It is first shown that i n an ordered ring placed in an external magnetic field, if the electro n is in the pair of time-reversed states as the ring geometry allows, the magnetic flux through the ring is quantized with flux quantum h/2e . Then we show that in a disordered one-dimensional ring placed in an external magnetic field, the electron is forbidden, by the potential v ariation due to the disorder, to be in the time-reversed state pair, a nd thus the AAS oscillations in magneto resistance cannot exhibit. The previous experiments on normal metal rings are analyzed to be in agre ement with our conclusion by specifying the diffusion-related one-dime nsion.