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The Hermitian part of the dipole-dipole interaction in infinite periodicarrays of two-level atoms yields an energy band of singly excited states. Inthis Letter, we show that a dispersion relation, $\omega_k-\omega_{k_\ex}\propto (k-k_{\ex})^s$, near the band edge of the infinite system leads to theexistence of subradiant states of finite one-dimensional arrays of $N$ atomswith decay rates scaling as $N^{-(s+1)}$. This explains the recently discovered$N^{-3}$ scaling and it leads to the prediction of power law scaling withhigher power for special values of the lattice period. For the quantum opticalimplementation of the Su-Schrieffer-Heeger (SSH) topological model in adimerized emitter array, the band-gap-closing inherent to topologicaltransitions changes the value of $s$ in the dispersion relation and alters thedecay rates of the subradiant states by many orders of magnitude.

Subradiant emission from regular atomic arrays: universal scaling of decay rates from the generalized Bloch theorem