  $\alpha$-cluster structures above double shell closures are among the
cornerstones for nuclear $\alpha$-cluster physics. Semi-microscopic cluster
models (SMCMs) are important theoretical models to study their properties. A
crucial ingredient of SMCM is the effective potential between the alpha cluster
and the doubly magic nucleus. We derive new double-folding potentials between
$\alpha$ clusters and doubly magic nuclei from soft local chiral
nucleon-nucleon potentials given by chiral effective field theory ($\chi$EFT)
at the next-to-next-to-leading order. The $\alpha$-cluster structures in
${}^{8}\text{Be}$, ${}^{20}\text{Ne}$, ${}^{44,52}\text{Ti}$, and
${}^{212}\text{Po}$ are explored to validate these new double-folding
potentials. The $\alpha$ decay of ${}^{104}\text{Te}$ is also studied in the
light of recent experimental results. Our study shows that double-folding
potentials from $\chi$EFT are the new reliable effective potentials for the
SMCM approach to $\alpha$-cluster structures above double shell closures, with
both conceptual and phenomenological merits.
