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Recently, unusual $\pi$ phase shifts in Little-Parks experiments performed ontwo systems derived from the layered superconductor 2H-TaS$_2$ were reported.These systems share the common feature that additional layers have beeninserted between the 1H-TaS$_2$ layers. In both cases, the $\pi$ phase shifthas been interpreted as evidence for the emergence of exotic superconductivityin the 1H layers. Here, we propose an alternative explanation assuming thatsuperconductivity in the individual 1H layers is of conventional $s$-wavenature derived from the parent 2H-TaS$_2$. We show that a negative Josephsoncoupling between otherwise decoupled neighboring 1H layers can explain theobservations. Furthermore, we find that the negative coupling can arisenaturally assuming a tunneling barrier containing paramagnetic impurities. Animportant ingredient is the suppression of non-spin-flip tunneling due tospin-momentum locking of Ising type in a single 1H layer together with theinversion symmetry of the double layer. In the exotic superconductivityscenario, it is challenging to explain why the critical temperature is almostthe same as in the parent material and, in the 4Hb case, thesuperconductivity's robustness to disorder. Both are non-issues in our picture,which also exposes the common features that are special in these two systems.

A mechanism for $\pi$ phase shifts in Little-Parks experiments: application to 4Hb-TaS$_2$ and to 2H-TaS$_2$ intercalated with chiral molecules