We develop a symmetry indicator framework to efficiently predict the topology of superlattice-induced minibands with spin-orbit coupling. Our algorithm requires input only from the parent material before the superlattice is applied. The simplification arises by assuming a perturbatively weak superlattice potential; however, our results extend beyond the perturbative regime as long as the superlattice-induced gaps remain open. We first consider a time-reversal- and inversion-symmetric system subject to a weak superlattice potential and derive a compact formula for the ${\mathbb{Z}}_2$ invariant of the lowest miniband. We then extend to time-reversal breaking systems and compute the Chern number. We apply our theory to selected transition-metal dichalcogenides, HgTe/CdTe quantum wells, and thin films of three-dimensional topological insulators and Dirac semimetals. We find topological superlattice bands can arise even from nontopological materials, broadening the pool of candidates for realizing topological flat bands. Our theory predicts which geometry and periodicity of superlattice will yield topological bands for a given material, providing a clear guiding principle for designing topological superlattice heterostructures.

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• Crystal symmetry
• Quantum spin Hall effect
• Spin-orbit coupling
• Superlattices
• Thin films
• Transition metal dichalcogenides
• Topology