Selective amplification and the charge conjugation symmetry in topological photonics

In systems with suitable symmetries, topologically protected states can arise that are immune to perturbations. I describe how the appearance of such states can be tailored by modifying symmetries in artificially engineered systems via loss and gain, in analogy to parity-time-symmetric systems. The interplay of these effects can be utilised for selective amplification in one and two dimensions, either of point defect states or of topological states in the bulk. All these systems happen to display a nonhermitian charge-conjugation symmetry, which combines aspects of charge conjugation in electronic systems and PT symmetry in optical systems. To illustrate the role of this useful symmetry in a different setting, I also discuss how topological states can emerge in lossy systems even when they are trivial in the conventional classification (which ignores losses).