Gauge-invariant thermal-gradient phase offsets in magnetic Josephson interferometers

This manuscript proposes a gauge-invariant mechanism by which a controlled nonequilibrium thermal gradient can generate a phase-quadrature response in magnetic Josephson interferometers. The central idea is that a magnetic weak link can convert a thermal gradient into an odd-in-gradient phase offset, observable as a horizontal displacement of the SQUID interference pattern, rather than merely as a change in interference visibility. The predicted response appears experimentally as an equivalent flux or magnetic-field shift and can be separated from ordinary heating-induced critical-current modulation by magnetic-field sweeps, lock-in quadrature analysis, gradient reversal, and arm-exchange controls.