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Planar arrays of magnetoinductively coupled rf SQUIDs belong to the emergentclass of superconducting metamaterials that encompass the Josephson effect.SQUID metamaterials acquire their electromagnetic properties from the resonantcharacteristics of their constitutive elements, i.e., the individual rf SQUIDs,which consist of a superconducting ring interrupted by a Josephson junction. Weinvestigate the response of a two-dimensional SQUID metamaterial to frequencyvariation of an applied alternating magnetic field in the presence of disorder,arising from critical current fluctuations of the Josephson elements; ineffect, the resonance frequencies of individual SQUIDs are distributed randomlyaround a mean value. Bistability is observed in the total current-frequencycurves both in ordered and disordered SQUID metamaterials; moreover,bistability is favoured by disorder through the improvement of synchronizationbetween SQUID oscillators. Relatively weak disorder widens significantly thebistability region by helping the system to self-organize itself and leads tonearly homogeneous states that change smoothly with varying frequency.Moreover, the total current of the metamaterial is enhanced compared with thatof uncoupled SQUIDs, through the synergetic action of coupling andsynchronization. Multistability of nearly homogeneous states allows themetamaterial to exhibit different magnetic responses corresponding to differentvalues of the magnetic permeability. At low power of the incident field,high-current states exhibit extreme diamagnetic properties corresponding tonegative magnetic permeability in a narrow frequency region.

Multistability and Self-Organization in Disordered SQUID Metamaterials