Damage-repair kinetics and phase stiffness in a site-diluted XY model: implications for irradiated superconductors

Abstract

A computational study of a phenomenological model. No experiment was performed and the model is not calibrated to any conductor. Prepared for submission to Superconductor Science and Technology. A two-dimensional XY lattice of the local superconducting phase, in which sites are damaged (pair breaking) at a rate that rises with local phase disorder and repaired at a stochastic rate, is simulated by kinetic Monte Carlo (engine verified bit for bit against the MyUncle framework, 10.5281/zenodo.21223569). What the study contains. (i) The mean-field reduction re-derived from the implemented update for the damaged fraction, with the bistable windows of both the rate equation and the discrete-time map, and a test of its closure against the lattice. (ii) Two-start tests and quasi-static ramps at baseline field, with all interval exceptions listed and Holm-corrected. (iii) A twist-response measurement of the phase stiffness of the non-equilibrium steady state (with winding numbers recorded), compared with the equilibrium fluctuation formula, and phase correlations C(r), for repair rules that preserve the U(1) symmetry. (iv) The competition between damage rate and phase relaxation (timescale parameter) and the discrete-time effects. (v) Finite-size scaling of the quenched dilution transition to L = 128, clustered damage, the BKT line T_BKT(f), and an illustrative mapping to displacement damage and annealing. Code, raw data and analysis: https://github.com/sandlerleon/damage-repair-xy-stiffness, archived at 10.5281/zenodo.23138195.