Topological split-ring resonator based metamaterials with PT symmetry relying on gain and loss

A one-dimensional metamaterial with parity-time (PT) symmetry that relies on balanced gain and loss is introduced, comprising magnetically coupled split-ring resonators (SRRs). A particular topology that combines a nontrivial (topological) dimer configuration with a trivial (nontopological) dimer configuration separated by a central SRR with neither gain nor loss is investigated. By focusing on the dynamical aspects of such a topological PT metamaterial (PTMM), the existence of topologically protected interface states which are localized at the central SRR is demonstrated numerically. The solution of the corresponding quadratic eigenvalue problem reveals that the protected state is actually a robust eigenmode of the topological PTMM, whose eigenvalue is isolated in the middle of the gap (midgap state) of the two-band frequency spectrum. Direct numerical simulations have been further used to determine the robustness and dynamic stability of these states in the parameter space of the dimerization strength and the gain-loss coefficient.