Dislocations are shown to be smooth at zero temperature because of the effective Coulomb-type interaction between kinks. Crossover to finite temperature rougnehing is suggested to be a mechanism responsible for the softening of he4 shear modulus rece
ntly observed by Day and Beamish (Nature, {bf 450}, 853 (2007)). We discuss also that strong suppresion of superfuidity along the dislocation core by thermal kinks can lead to locking in of the mechanical and superfluid responses.
More than half a century ago Penrose asked: are the superfluid and solid state of matter mutually exclusive or do there exist supersolid materials where the atoms form a regular lattice and simultaneously flow without friction? Recent experiments pro
vide evidence that supersolid behavior indeed exists in Helium-4 -- the most quantum material known in Nature. In this paper we show that large local strain in the vicinity of crystalline defects is the origin of supersolidity in Helium-4. Although ideal crystals of Helium-4 are not supersolid, the gap for vacancy creation closes when applying a moderate stress. While a homogeneous system simply becomes unstable at this point, the stressed core of crystalline defects (dislocations and grain boundaries) undergoes a radical transformation and can become superfluid.
