Condensation mechanism of high-$T_c$ cuprates: the key role of pairon excitations

TL;DR

This paper proposes a new condensation mechanism for high-$T_c$ cuprates involving pairon excitations, linking the energy gap to spin exchange energy and deriving a formula for $T_c$ that depends on condensation energy.

Contribution

It introduces a formalism connecting the energy-dependent gap function to pairon excitations and provides a quantitative model for $T_c$ based on condensation energy, applicable across doping levels.

Findings

The energy gap $oldsymbol{ ext{Δ}(E)}$ is proportional to the effective spin exchange energy $oldsymbol{J_{eff}}$.

The critical temperature $oldsymbol{T_c}$ is proportional to the condensation energy per pair $oldsymbol{eta_c}$.

A mini-gap $oldsymbol{ ext{δ}_M \, ext{≈ 1 meV}}$ in the excitation spectrum explains the Bose statistics of pairon excitations.

Abstract

In this article we show that the condensation mechanism in cuprates involves the strong coupling of the condensate to pairon excited states. We present an accessible formalism that significantly extends our previous work, providing a theoretical basis for the energy-dependent gap function $\Delta(E)$. The latter is proportional to the effective spin exchange energy, $J_{eff}$, with no retardation effects, such as the case of spin-fluctuation or phonon mediated couplings. The fundamental parameters of the superconducting (SC) state are the condensation energy per pair, $\beta_c$, and the antinodal energy gap, $\Delta_p$, which are quantitatively extracted by fitting the cuprate quasiparticle spectrum from tunneling experiments. An explicit formula for the critical temperature is also derived in the model. Valid for any doping, we find $T_c$ to be proportional to $\beta_c$, and not the gap $\Delta_p$, in sharp contrast to conventional SC. The numerical factor $\beta_c/k_BT_c\simeq 2.24$ originates from pair excitations of the condensate, following Bose statistics, with a mini-gap $\delta_M \simeq 1\,$meV in the excitation spectrum. These results strongly suggest that the same `all-electron' mechanism is at work all along the $T_c$-dome.