Abstract
A topological approach is used to show that the flux periodicity of any practical single-junction rf SQUID or double-junction dc SQUID device is one flux quantum (Φ0). The flux periodicity is independent of the number of superconducting loops and circuit inductances. The topological point of view explains how multihole configurations can be derived from a toroidal one. Weak links are considered as topological switches that allow magnetic flux lines to pass from one homotopic class of loops to another. In addition to rf SQUIDs in the hysteretic or nonhysteretic regime, we also consider resistive and dc SQUIDs. Some special cases are also introduced where the flux periodicity is not Φ0, due to special nonlinear behavior of the weak link, due to coupling to a resonant circuit, or because of a great number of weak links in the superconducting circuit. The flux periodicity of a SQUID is a property of the weak link itself, and not of the inductances connected to it. Only the number of weak links and their mutual connection in series or parallel can change the fundamental flux periodicity of the device.
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