Eur. Phys. J. B (2025) 98: 190
https://doi.org/10.1140/epjb/s10051-025-01036-8

Regular Article - Solid State and Materials

Singlet-bond superconductivity theory of the phase diagrams of cuprate high-temperature superconductor

Department of Physics, Niigata University, 950-2181, Niigata, Japan

^a hh.kaga@gmail.com

Received: 5 March 2025
Accepted: 1 September 2025
Published online: 16 September 2025

Abstract

This paper shows that the singlet-bond (SB) superconductivity theory can explain the phase diagram of cuprate high-temperature superconductor and presents the Ginzburg-Landau (GL) free energy formulation of the SB theory together with the London penetration depth $\lambda$ and the GL coherence length $\xi$. The experimental temperature-doping $T-\delta$ phase diagrams covering the underdoped and overdoped regimes are shown to result from various physical phenomena in the SB superconductivity theory. There is the monotonically increasing doping-dependent coherence onset temperature $T_{\mathit{coh}}$ between the superconducting transition temperature $T_c$ and the monotonically decreasing pseudogap onset temperature $T_{}^{\ast }$, ($T_c<T_{\mathit{coh}}<T_{}^{\ast }$), becoming the condensation onset temperature $T_0$, ($T_{\mathit{coh}}=T_0$), in the underdoped regime. When $T_{\mathit{coh}}$ reaches $T_{}^{\ast }$, the $T_0$ temperature switches over from $T_{\mathit{coh}}$ to $T_{}^{\ast }$ temperature, becoming highest (also $T_c$ becoming highest) at the intersection at the optimal doping ${\delta }_m(\sim 0.15)$, and then follows $T_{}^{\ast }$ temperature in the overdoped regime. $T_c$ value is scaled by $T_0$ value in the same expression throughout the two doing regimes. At the end ${\delta }_{\mathit{pg}}(\sim 0.2$) of the pseudogap phase the overdoped strong-coupling superconductivity crossovers to the weak-coupling BCS superconductivity. The pseudogap phase PG+ below $T_0$ is different from that PG above $T_0$ because in the background of the PG+ phase movable SB-pairs exist and easily lead, with a small kinetic energy gain, to a variety of collective states such as CDW order. The GL free energy formulation is more suitable for the SB superconductivity than for the BCS superconductivity since it can be applied for the whole temperature range $0<T<T_0$ due to the local nature of SB order-parameter. The GL free energy of the SB theory predicts the linear temperature dependence of $\frac{1}{{\lambda }^2(T)}=\frac{1}{{\lambda }^2(0)}(1-aT)$ with $a\sim 6.4\times {10}^{-3}{K}^{-1}$ and $\lambda (0)\sim {10}^{3}A$ for $\delta =0.15$ and the T-independent GL coherence length $\xi \sim 1A$, both of which are in good agreement with experiments.