  Regular lattices comprising superconducting quantum interference devices
(SQUIDs) form magnetic metamaterials exhibiting extraordinary properties,
including tunability, dynamic multistability, and negative magnetic
permeability. The SQUIDs in a metamaterial interact through nonlocal, magnetic
dipole-dipole forces that makes it possible for counter-intuitive dynamic
states referred to as chimera states to appear; the latter feature clusters of
SQUIDs with synchronous dynamics which coexist with clusters exhibiting
asynchronous behavior. The spontaneous appearance of chimera states is
demonstrated numerically for one-dimensional SQUID metamaterials driven by an
alternating magnetic field in which the fluxes threading the SQUID rings are
randomly initialized; then, chimera states appear generically for sufficiently
strong initial excitations, which exhibit relatively long lifetimes. The
synchronization and metastability levels of the chimera states are discussed in
terms of appropriate measures. Given that both one- and two-dimensional SQUID
metamaterials have been already fabricated and investigated in the laboratory,
the presence of a chimera state could in principle be detected with presently
available experimental setups.
