Quantum Interference in a Series of Metallic Rings in a Magnetic Field

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Abstract
The role of quantum interference of free electrons in a one‐dimensional normal metal ring in a magnetic field is considered. Calculations of the transmission between two perfect wires connected to the ring through ideal splitters are presented. The transmission of the single ring is a symmetric function of the enclosed magnetic flux and oscillates with the basic period hc/e. However, in an infinite series of rings the interference conditions vary from ring to ring which leads to averaging of the transmission. The localization length shows oscillations with the period hc/2e. Recent resistance measurements on small metallic systems in a magnetic field are discussed in the framework of this model.