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

Abstract

Understanding the dynamical origin of high--temperature superconductivity remains a central challenge of strongly correlated quantum matter. Conventional approaches to quantum criticality assume overdamped Markovian dissipation governed by Ohmic Landau damping. Here we show that infrared collective dynamics is instead generically controlled by the time--scale density of states (TDOS) of relaxation modes. Within the Martin--Siggia--Rose--Janssen--De Dominicis formalism, we derive an exact spectral representation of the collective susceptibility in terms of the TDOS. A finite infrared TDOS defines a new universality class of memory--dominated critical dynamics characterized by long--time kernels $K(t)\sim1/t$ and nonanalytic dynamical response. This spectral reorganization produces a strong infrared amplification of the particle--particle channel, converting the marginal instabilities of BCS and Eliashberg theories into algebraic superconducting transitions. As a result, the transition temperature scales linearly with the infrared spectral weight of slow collective modes, naturally yielding superconducting domes and Uemura scaling without invoking bosonic glue or fine tuning. The same slow--mode reservoir governs anomalous normal--state dynamics, including long--time correlations and strange--metal behavior, providing a unified description of thermodynamic and dynamical phenomena in correlated superconductors. Our results establish dynamical spectral organization as a fundamental principle of quantum critical matter and identify memory--dominated criticality as a generic route to high--temperature superconductivity.

Figures (3)

• Figure 1: Dynamical universality map of correlated quantum matter. (a) Infrared time--scale density of states $\rho(\lambda)$ defining distinct dynamical universality classes. Vanishing TDOS yields conventional Hertz--Millis and phonon dynamics, marginal spectra produce Ohmic damping, while a flat TDOS defines memory--dominated criticality. (b) Corresponding long--time kernels in the time domain, ranging from Markovian dissipation to non-Markovian power--law memory. (c) Physical consequences of memory--dominated criticality, including algebraic pairing enhancement, superconducting domes, Uemura scaling, strange metal transport, and long--time noise correlations.
• Figure 2: Infrared renormalization-group flow of the Cooper-channel interaction. Shown schematically is the flow of the dimensionless pairing coupling $g$ under infrared coarse graining. Ohmic Landau damping of collective modes produces marginal logarithmic growth, $dg/dl\sim g^2$, characteristic of conventional Eliashberg theory (blue). In contrast, memory--dominated dynamics generated by a flat relaxation--rate density of states yields a relevant infrared instability, $dg/dl=\alpha g$, leading to algebraic amplification of the pairing interaction (orange). The slow--mode reservoir therefore dynamically enhances intrinsic electronic pairing tendencies rather than merely renormalizing a fixed microscopic coupling.
• Figure 3: Experimental consequences of memory--dominated critical dynamics. (a) Superconducting dome emerging from truncation of the slow--mode reservoir away from criticality. The transition temperature follows $T_c(p)\sim E_{\rm pair}\rho_0(p)$ and is maximal near the correlated critical point $p_c$, where infrared spectral weight of collective relaxation modes is largest. Suppression of $T_c$ on both sides arises solely from the finite infrared extent of the slow--mode reservoir, without invoking competing orders or fine tuning. (b) Uemura scaling collapse between superconducting transition temperature and superfluid stiffness, $T_c\propto\rho_s$. Both pairing strength and phase coherence are controlled by the same infrared spectral weight $\rho_0$ of slow collective modes, yielding universal linear scaling across material families.