Enhancement of Tc in Oxide Superconductors: Double-Bridge Mechanism of High-Tc Superconductivity and Bose-Einstein Condensation of Cooper Pairs

TL;DR

The paper proposes a double-bridge mechanism for high-$T_c$ superconductivity in ionic-bonded oxides, where bridge-I promotes strong Cooper-pair formation and bridge-II mediates an attractive interaction between Cooper pairs to drive Bose-Einstein condensation. Within the Bose-Einstein condensation framework for interacting bosons, it derives that the ideal critical temperature scales as $T_c^0 \propto \frac{n_s^{2/3}}{m^*}$ and that attractive inter-pair interactions raise $T_c$ via $T_c = T_c^0\left(1-3.426\frac{a}{\lambda_0}\right)$ with $\lambda_0=\frac{h}{\sqrt{2\pi m^* k_B T_c^0}}$, highlighting the roles of Cooper-pair density $n_s$, effective mass $m^*$, and scattering length $a$. The authors argue that maximizing $n_s$, minimizing $m^*$, and tuning $a$ to strengthen net attraction can substantially raise $T_c$, potentially toward room temperature, and claim universality of this design principle across cuprates, nickelates, iron-based, and other ionic superconductors. Overall, the work provides a directional framework for engineering higher $T_c$ by manipulating microscopic pairing and condensation parameters in ionic oxide superconductors.

Abstract

The cuprate Hg0.8Tl0.2Ba2Ca2Cu3O8.33 exhibits the highest superconducting transition temperature Tc of 138K. Achieving superconductivity at even higher temperatures, up to room temperature, represents the ultimate dream of humanity. As temperature increases, Cooper pairs formed through weak electron-phonon coupling will be disintegrated by the thermal motion of electrons, severely limiting the enhancement of Tc. It is imperative to explore new strong-coupling pairing pictures and establish novel condensation mechanism of Cooper pairs at higher temperature. Based on our recently proposed groundbreaking idea of electron e- (hole h+) pairing bridged by oxygen O (metal M) atoms, namely, the eV-scale ionic-bond-driven atom-bridge (bridge-I) e--O-e- (h+-M-h+) strong-coupling itinerant Cooper pairing formed at pseudogap temperature T*>Tc in ionic oxide superconductors, we further discover that there is an attractive interaction between two Cooper pairs induced by the bridge atom (bridge-II) located between them. It is this attraction mediated by the bridge-II atoms that promotes all the Cooper pairs within the CuO2 plane to hold together and enter the superconducting state at Tc finally. Moreover, according to the Bose-Einstein condensation theory, we find that Tc is inversely proportional to the effective mass m* of Cooper pairs, directly proportional to n2/3s (ns: the density of Cooper pairs), and linearly increases with the scattering length a<0 due to attraction between two Cooper pairs. Therefore, according to our double-bridge mechanism of high-Tc superconductivity, increasing the attraction between Cooper pair and bridge-II atom, ensuring that ns takes the optimal value, and minimizing the effective mass of the Cooper pairs are the main approaches to enhancing Tc of ionic-bonded superconductors, which opens up a new avenue with clear direction for designing higher Tc superconductors.

Figures (4)

• Figure 1: (a) The 4$a$-period Cu-bridged (bridge-I) hole Cooper-pair h^+-Cu-h^+ stripe phase in the CuO2 plane Kohsaka2007Vojta2008shi2025, in which two Cooper pairs are attracted to each other through the O$^{x-}$ (1$<x$$\leq$2) anion as a bridge (bridge-II). (b) The major direct and O-bridged correlation mechanisms between two h^+-Cu-h^+ hole Cooper pairs and the corresponding interaction energy scale. Similar to the h^+-Cu-h^+ pairs, the correlation mechanisms can also be found for the Cu-bridged correlation of the O-bridged e^--O-e^- electron Cooper pairs.
• Figure 2: The double-bridge mechanism of high-$T_c$ superconductivity in cuprates. (a) The strong Coulomb attraction exerted by the O$^{x-}$ (1$<x$$\leq$2) anion, acting as a bridge (bridge-II), on its two nearest-neighboring Cu-bridged (bridge-I) hole Cooper pairs h^+-Cu-h^+, together with the strong Coulomb repulsion between Cu$^{y+}$ (1$<y<$2) cation and the Cooper pair around it to push the h^+-Cu-h^+ hole pair towards the nearest-neighboring O$^{x-}$ anion, is equivalent to an indirect strong mutual attraction between the two h^+-Cu-h^+ pairs. When $T_c<T<T^*$ ($T^*$: the pseudogap temperature), this indirect strong mutual attraction induced by the bridge-II atom reaches a balance with the direct Coulomb repulsion between the two h^+-Cu-h^+ pairs and the $equivalent$$repulsion$ between the O$^{x-}$ anions and the h^+-Cu-h^+ pairs due to the requirement of ionic binding for increasing the valence state of ions to reduce the total energy of the crystal and to keep the structural stability (see Fig. 2(a) shi2025), as described in Fig. \ref{['fig:1']}(b). When $T$$\leq$$T_c$, the decrease in the kinetic energy of electrons in the electron cloud surrounding the O$^{x-}$ anions weakens the electrons' ability to escape the binding of the oxygen nuclei. This leads to a slight increase in the charge amount Q (negative valence state) carried by the O$^{x-}$ anions, i.e., $Q$$\rightarrow$$Q$+$\delta$$Q$ with $\delta$$Q$ a small quantity, which will also be influenced by the transition of Cooper pairs from their excited states to the ground state (see text). The original balance is thus disrupted. Similar to O$^{x-}$ anion, the positive valence state of the Cu$^{y+}$ cation will also be enhanced slightly at $T$$\leq$$T_c$. The Coulomb attraction between the O$^{x-}$ anion and its two nearest-neighboring h^+-Cu-h^+ Cooper pairs thus increases, causing a net attraction between two h^+-Cu-h^+ Cooper pairs. According to the BCS-BEC crossover theory (see Fig. \ref{['fig:3']} in End Matter) Pitaevskii2016Chen-RevModPhys-2024, it is precisely under the driving of this net attraction that BEC occurs in the two h^+-Cu-h^+ Cooper pairs. (b) According to Coulomb's law, for two h^+-Cu-h^+ Cooper pairs located on the same -Cu-O-Cu- chain and separated by several lattice constants, their strong mutual attractions with their respective nearest-neighboring O$^{x-}$ anions are much greater than the interactions with other more distant ions. The net effect is equivalent to an indirect mutual attraction between the two h^+-Cu-h^+ Cooper pairs. Similar to (a), at $T$$\leq$$T_c$, these two h^+-Cu-h^+ Cooper pairs can also undergo BEC through the O-bridge. (c) Combining (a) and (b), and taking into account the hole stripe phase, all Cu-bridged (bridge-I) h^+-Cu-h^+ Cooper pairs within the CuO$_2$ planes "hold hands" with each other through the oxygen bridges (bridge-II) and undergo BEC to enter the superconducting state—the double-bridge mechanism of high-$T_c$ superconductivity. This picture fully demonstrates the true physical beauty of the high-$T_c$ superconducting mechanism. For O-bridged (bridge-I) e^--O-e^- Cooper pairs, a similar double-bridge picture can also be established by way of Cu$^{y+}$(1$<$$y$$<$2) cations as bridges (bridge-II) for BEC of e^--O-e^- pairs.
• Figure 3: The BCS-BEC crossover phase diagram in high-$T_c$ cuprates Chen-RevModPhys-2024, in which the attraction between the Cooper pairs with zero spin is of crucial importance for the condensation of Cooper pairs.
• Figure 4: The superconducting critical temperature $T_c$ as a function of the scattering length $|a|$ ($a<$0) due to the indirect net attraction between two Cu-bridged (bridge-I) h+-Cu-h+ hole Cooper pairs mediated by the O-bridge (bridge-II), derived from Eq. (\ref{['eqn:3']}), by using the parameters summarized in Table \ref{['tbl:1']} for cuprates I-VI. It indicates a new and clear way to enhance $T_c$, i.e., by improving the indirect attraction between two Cooper pairs with small effective mass $m^*$ under the optimal concentration $n_s$. This would be extremely encouraging for maximizing $T_c$.