Phase-field model of strain effect on superconducting transitions and mesoscale pattern formation

Despite the extensive research on superconductivity and related phenomena, the effect of the mechanical strain on the superconducting transition and mesoscale pattern formation of a material is not well understood. Here, we develop a phase -field model of strain effect on superconducting phase transitions and vortex pattern formation by coupling linear elasticity with a Time -Dependent Ginzburg-Landau (TDGL) model for superconducting phase transitions. We implement an efficient iterative method based on finite -element discretization for solving the coupled TDGL equation for the complex electronic order parameter, the magnetic equation for the vector magnetic potential, and the mechanical equilibrium equation for the mechanical displacements with arbitrary elastic boundary conditions. We study and discuss the effects of epitaxial strains on the superconducting transition temperature, critical magnetic field, and vortex pattern formation in a superconducting thin film.