  The unique superflow-through-solid effect observed in solid Helium-4 and
attributed to the quasi-one-dimensional superfluidity along the dislocation
cores exhibits two extraordinary features: (i) an exponentially strong
suppression of the flow by a moderate increase in pressure, and (ii) an unusual
temperature dependence of the flow rate with no analogy to any known system and
in contradiction with the standard Luttinger liquid paradigm. Based on ab
initio and model simulations, we argue that the two features are closely
related: Thermal fluctuations of the shape of a superclimbing edge dislocation
induce large, correlated, and asymmetric stress fields acting on the superfluid
core. The critical flux is most sensitive to strong rare fluctuations and
hereby acquires a sharp temperature dependence observed in experiments.
