A mechanism for nonmonotonic $T_{c,max}(n)$ in multilayer cuprates

Abstract

We propose an explanation of the observed dependence of the maximal critical temperature $T_{c,max}$ on the number of conducting layers $n$ in layered copper-oxide superconductors within the preformed pair mechanism. Copper-oxygen planes fine-tune the lattice anisotropy and regulate the balance between the attractive and kinetic energies of carrier holes. To maximize the Bose-Einstein condensation temperature, real-space pairs must be compact and light at the same time. Generally, $T_{c,max}$ increases between $n = 1$ and $n = 3$ because pairs become lighter. For $n > 3$, the rising kinetic energy weakens the pairs, leading to inflated pair volumes and reduced $T_{c,max}$. By varying model parameters, the peak of $T_{c,max}(n)$ can be tuned to $n = 2$, $n = 3$, or $n > 3$. We also discuss strategies for using this knowledge to boost $T_{c,max}$ beyond the current record of 138 K.

Figures (32)

• Figure 1: The highest reported $T_c$ for the seven cuprate families and one nickelate family of superconductors. Acronyms and data sources are given in Table \ref{['MLH:tab:one']}. The dashed line marks $T_c = 110$ K for the "infinite-layer" superconductor (Sr,Ca)CuO$_2$Azuma1992. The dot-dashed line marks $T_c = 40$ K of the "infinite-layer" superconductor ReNiO$_2$Chow2025.
• Figure 2: Qualitative explanation of nonmonotonic $T_{c,{\rm max}}(n)$. (a) A multilayer lattice with $n = 3$. (b) Qualitative dependence of the attractive energy $V$ and kinetic energy $K$ on the number of layers $n$. (c) The ratio $V/K$ decreases with $n$, approaching the pairing threshold. (d) As the system approaches this threshold, the pair $z$ mass decreases but the pair volume increases. According to Eq. (\ref{['MLH:eq:two']}), the close-packing temperature $T^{\ast}_{\rm cp} \propto T_{c,{\rm max}}$ exhibits a broad maximum.
• Figure 3: Schematic evolution of $T_{c}(p)$ with doping in multilayer cuprates. The superconducting dome is asymmetric Honma2008. Pairs are close-packed at optimal hole doping $p_{0}$. Note that the pairs are larger near $p_0$ than in the underdoped regime, $p < p_{0}$. In the overdoped regime, $p > p_{0}$, the pairs lose individuality and dissolve into a Fermi sea.
• Figure 4: Schematic structure of multilayer cuprates. Horizontal lines represent CuO$_2$ planes, and gray rectangles denote "charge reservoir layers". Note that the $n = 3, 4$ members contain two distinct types of planes, shown by solid and long-dashed lines, whereas the $n = 5$ member has three distinct types, shown by solid, long-dashed, and short-dashed lines.
• Figure 5: (c) The close-packing BEC temperature, Eq. (\ref{['MLH:eq:two']}), and its two constituents: (a) the $c$-axis pair mass $m^{\ast}_{z}$, and (b) the pair volume $\Omega_{p}$ in the $n = 1$ ("tetragonal") attractive Hubbard model; see Appendix \ref{['MLH:sec:app:b']} and Kornilovitch2024. Note how the divergence of $m^{\ast}_{z}$ as $t^{\prime} \to 0$ and the divergence of $\Omega_{p}$ as $t^{\prime} \to t^{\prime}_{\rm pairing \: threshold}$ together produce an optimal $t^{\prime}$ at which $T^{\ast}_{\rm cp}$ is maximized Kornilovitch2015. The transition from $n = \infty$ to $n = 1$ corresponds to moving away from this optimal $t^{\prime}$ toward smaller values of $t^{\prime}$. The legend in the left panel applies to all panels.