Preformed Cooper pairing and the uncondensed normal-state component in phase-fluctuating monolayer cuprate superconductivity

Abstract

We develop a self-consistent microscopic framework beyond mean-field theory for monolayer cuprate superconductivity. It couples fermionic quasiparticles with collective phase dynamics to treat the gap and superfluid stiffness. The phase sector explicitly incorporates both smooth bosonic Nambu-Goldstone phase fluctuations, renormalized by long-range Coulomb interactions, and topological BKT-type vortex-antivortex fluctuations. The required input is the correlated single-particle spectral function, enabling direct interfacing with Hubbard-type models. The theory provides access to key superconducting observables, including $T$-dependent gap and phase stiffness, gap-closing temperature $T_{\rm os}$, and transition temperature $T_c$, across wide ranges of doping. Using a solvable interaction model as input, our simulations reveal several important features consistent with experimental observations in cuprate superconductors: a $d$-wave superconducting dome in $T$-$p$ phase diagram with a shoulder-like anomaly in underdoped regime, a pronounced separation between $T_c$ and $T_{\rm os}$ signaling preformed Cooper pairing, a finite uncondensed normal component persisting even at $T=0$, and the onset temperature $T_{\rm on,vortex}$ of vortex signals, offering a consistent understanding of how strong correlations and phase fluctuations cooperate to shape high-$T_c$ superconductivity.

Figures (2)

• Figure 1: Doping evolution of the Fermi surface from underdoped to overdoped regimes at $T\approx3\,\mathrm{mK}$. We take ${{\mathcal{V}}}=1.15t$worm24fermiUvalue.
• Figure 2: ( a) Transition temperature $T_c^{\rm MF}$ for $d_{x^2-y^2}$-, $d_{xy}$-, and $s$-wave pairings from mean-field theory (without fluctuations). ( b) Zero-temperature SC gap within mean-field (MF) theory and the phase-fluctuating (PF) framework. The inset shows $|\Delta(T)|$ in the PF framework. ( c) Bare (red) and BKT-renormalized (blue) phase stiffness. The straight line indicates $2T/\pi$, where the discontinuous drop of superfluid stiffness occurs. ( d) Phase diagram of the gap-closing temperature $T_{\rm os}$ and transition temperature $T_c$ as a function of doping within the PF framework. The inset magnifies the shoulder-like feature on the $T_c$-$p$ dome. ( e) Zero-temperature superfluid stiffness $f_s(0)$, reflecting $n_s(0)/m^*$, within MF and the PF framework, and normal-state component $f_n(0)$. ( f) Ratio $f_s(0)/|\Delta(0)|$, coherence length $\xi_0$ and temperature difference $T_c^{\rm MF}-T_c^{\rm PF}$.