Historical Path Programming of Superconducting Order Parameters: A Unifying Framework and a Decisive Experimental Prospect

Abstract

The prevailing paradigm in superconductivity, rooted in the Ginzburg-Landau theory of 1950, assumes that the superconducting order parameter is uniquely determined by the current thermodynamic state variables—temperature, pressure, and magnetic field. Here we synthesize recent experimental discoveries across multiple superconducting families—kagome superconductors, infinite-layer nickelates, and cuprates—and demonstrate that each exhibits an unexplained "memory" of its historical path in parameter space. We propose that these phenomena are manifestations of a universal geometric principle: the superconducting order parameter is a path functional, not a state function. We introduce a historical weighting factor W[γ] that encodes path-dependent accumulation of quantum phase memory. This framework simultaneously accounts for: (i) thermal-history modulation of Josephson effects in CsV₃Sb₅, (ii) the "normal-state memory" of superconducting diode polarity in CsV₃Sb₅, (iii) the retention of pressure-enhanced superconductivity via pressure-quench protocols in Hg-1223 cuprates, (iv) the anti-correlation between magnetic exchange and Tc in nickelates, and (v) the unconventional two-gap behaviour in CsV₃Sb₅ that defies the standard multiband picture. We further propose a decisive experimental prospect—a closed loop in the (T,H) parameter space confined entirely within the superconducting and charge-density-wave (CDW) temperature range (2.0 K ↔ 8 K)—that would directly probe non-trivial holonomy. A quantitative discriminator—linear scaling of the deviation with loop area—distinguishes the proposed framework from conventional trapped-flux scenarios. The anomalies are not anomalies; they are the fingerprints of history, written into the quantum state.

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