Experimental Signatures of a Memory-Dressed Cooper-Pair Field in Antinodal ARPES

Abstract

Antinodal angle-resolved photoemission spectroscopy (ARPES) in cuprate superconductors reveals a broad incoherent background alongside a temperature-dependent superconducting contribution. We show that both features are naturally captured by a single family of parabolic cylinder functions (PCFs). First, the broad antinodal background in \BiCuprate\ is well described by a primitive PCF branch of the form $e^{-z^2/4}D_{-1/2}(z)$. Second, a superconductivity-associated component isolated via time-resolved ARPES subtraction follows a distinct $D_{3/2}$ branch. Third, the same $D_{3/2}$ structure is recovered in equilibrium temperature differences and across doping series. These findings motivate the minimal decomposition $\rho(E,T)=\rho_{\rm BG}(E,T)+\rho_{\rm SC}(E,T)$, where the superconductivity-associated spectral weight scales as $A_{\rm SC}(T)\propto |\Delta(T)|^2$. Dynamically, these branches originate from a Cooper-pair field with finite temporal memory: a smooth memory kernel generates a leading Gaussian temporal envelope $\exp(-t^2/2\tau_G^2)$ at short times, while algebraic many-body prefactors select the PCF branch index. If the finite-memory and algebraic incoherent dressing is formally removed, the resulting structure connects to the standard Bogoliubov/BCS spectrum. The main conclusion is that the incoherent antinodal continuum and the longer-lived superconductivity-associated component are distinct projections of a common memory-dressed pair field.