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

Abstract

Neutron damage lowers the transition temperature of REBCO conductors approximately linearly with displacement damage, and annealing recovers part of it, implicating phase stiffness. We model this competition as a two-dimensional XY lattice of the superconducting phase whose sites are damaged at a rate rising with local phase disorder and repaired stochastically, simulated by kinetic Monte Carlo. A mean-field reduction predicts bistability; the lattice shows no hysteresis or dependence on the initial state in the ranges tested (L ≤ 64) because the closure of the reduction fails. At zero field, symmetry-preserving repair restores spontaneous coherence and a twist-response stiffness (validated on clean and diluted lattices) above an apparent threshold in the repair-to-damage ratio, bracketed by finite-size scans (L ≤ 96) at ρ between 7.00 and 7.75 (ρ between 5.50 and 6.00 with neighbor-phase repair), against ρ ≈ 2.5 without feedback; the equilibrium formula underestimates the driven stiffness by up to 30%. Numerically, ρ controls the state ever better, as damage slows relative to phase relaxation. Finite-size analysis of random dilution estimates the stiffness loss at f ≈ 0.25 ± 0.01; clustered damage tolerates more. An illustrative effective mapping gives approximately ten model sites per dpa. The model is uncalibrated.