Abstract
We study within the Ginzburg-Landau (GL) theory of phase transitions how elastic deformations in a supersolid lead to local changes in the supersolid transition temperature. The GL theory is mapped onto a Schr\"odinger-type equation with an effective potential that depends on local dilatory strain. The effective potential is attractive for local contraction and repulsive for local expansion. Different types of elastic deformations are studied. We find that a contraction (expansion) of the medium that may be brought about by either externally applied or internal strain leads to a higher (lower) transition temperature as compared to the unstrained medium. In addition, we investigate edge dislocations and illustrate that the local transition temperature may be increased in the immediate vicinity of the dislocation core. We remark on the effects of shear screening induced by dislocation motion. Our analysis is not limited to supersolidity. Similar strain effects should also play a role in superconductors. Non-uniformly strained superconductors may thus exhibit a similar distribution of smeared local transition temperatures.
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