Memory-Dominated Quantum Criticality as a Universal Route to High-Temperature Superconductivity

Understanding the dynamical origin of high-temperature superconductivity remains a central challenge in strongly correlated quantum matter. Near quantum criticality, diverging correlation times reorganize the infrared dynamics into a scale-free continuum of collective relaxation processes. We show that the infrared behavior of interacting electrons is generically controlled by the relaxation-rate spectrum of the underlying many-body dynamics. Starting from a microscopic fermionic theory, we derive that the Cooper-channel kernel admits a universal spectral representation in terms of the time-scale density of states (TDOS) of collective decay modes, without invoking a specific bosonic mediator. The superconducting instability follows directly from the vanishing of the quadratic kernel via a standard ladder resummation and Thouless criterion, with the pairing interaction determined entirely by the infrared structure of the relaxation spectrum. A finite TDOS at vanishing relaxation rate produces a memory-dominated regime characterized by long-time kernels $K(t)\sim 1/t$ and logarithmic enhancement of the retarded pairing interaction, leading to a BCS-like exponential transition scale set by infrared spectral weight. More generally, infrared-singular spectra generate power-law response and algebraic enhancement of the transition scale. The same relaxation spectrum controls normal-state dynamics, giving rise to long-time correlations, non-Markovian response, and strange-metal behavior. These results identify the spectral organization of relaxation modes as a universal organizing principle of quantum critical matter and establish memory-dominated criticality as a natural mechanism for enhanced pairing.