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We analyse the emergence of unphysical superluminal group velocities inSu--Schrieffer--Heeger (SSH) parity-time ($\mathcal{PT}$) symmetric chains, andexplore the origins of such a behaviour. By comparing the band structure of aninfinite loss-gain SSH chain with that of a one-dimensional Bragg stack, wefirst exclude insufficient coupling consideration in the tight-bindingdescription as the cause of group-velocity divergence. We then focus onmaterial dispersion, and show that indeed, restoring causality in thedescription of both the lossy and the gain components resolves the problem andrecovers finite group velocities, whose real part can only exceed the speed oflight in vacuum when accompanied by a significant imaginary part. Our analysisintroduces thus the required practical limits in the performance of common$\mathcal{PT}$-symmetric systems.

Fundamental issues with light propagation through $\mathcal{PT}$-symmetric systems