Superconductivity: quantum uncertainty of the number of carriers and stability of the superconducting phase

The article addresses the conceptual link between quantum uncertainty in the number of charge carriers and the stability of the macroscopic superconducting phase. It is shown that a condensate of Cooper pairs characterized by a well-defined global phase is mathematically equivalent to a superposition of states with different pair numbers, so that local charge is effectively delocalized across the condensate. Building on this premise, the paper develops the notion of superconductor polarizability as a parameter governing the energetic cost of charge redistribution and, consequently, the critical characteristics of the material – critical current Ic and critical field Hc. Four classes of systems in which number-phase fluctuations are particularly pronounced are examined: thin films, granular superconductors, cuprates, and high-pressure hydrides. Experimental techniques for detecting these fluctuations (STM/STS spectroscopy, impedance spectroscopy, noise measurements) and the relevant theoretical frameworks (BCS theory, Ginzburg–Landau theory, strong-correlation models) are reviewed. The conclusion argues that superconductivity stability is governed by the balance between phase coherence and the energetic penalty for charge localization, and justifies the requirement for a comprehensive assessment of phase stiffness when evaluating claims of high-temperature superconductivity.