Multistability and self-organization in disordered SQUID metamaterials

Abstract

Planar arrays of magnetoinductively coupled rf SQUIDs (Superconducting QUantum Interference Devices) belong to the emergent class of superconducting metamaterials that encompass the Josephson effect. These SQUID-based metamaterials acquire their electromagnetic properties from the resonant characteristics of their constitutive elements, i.e., the individual rf SQUIDs. In its simplest version, an rf SQUID consists of a superconducting ring interrupted by a Josephson junction. We investigate numerically the response of a two-dimensional rf SQUID metamaterial with respect to the driving frequency of an externally applied alternating magnetic field in the presence of disorder arising from critical current fluctuations of the Josephson elements; in effect, the resonance frequencies of individual SQUIDs are distributed randomly around a mean value. Bistability is observed in the current amplitude–frequency curves both in ordered and disordered SQUID metamaterials; moreover, bistability is favored by disorder through the improvement of synchronization between SQUID oscillators. Relatively weak disorder widens significantly the bistability region by helping the system to self-organize and leads to nearly homogeneous states that change smoothly with varying driving frequency. Also, the total current of the metamaterial is enhanced, compared with that of uncoupled SQUIDs, through the synergetic action of coupling and synchronization. The existence of simultaneously stable states that provide either high or low total current, allows the metamaterial to exhibit different magnetic responses that correspond to different values of the effective magnetic permeability. At low power of the incident field, high current amplitude states exhibit extreme diamagnetic properties corresponding to negative magnetic permeability in a narrow frequency interval.