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

TL;DR

This paper explains how the maximum critical temperature in layered cuprate superconductors depends on the number of layers, highlighting the balance between pairing strength and kinetic energy, and suggests ways to enhance $T_{c,max}$.

Contribution

It introduces a model explaining the nonmonotonic dependence of $T_{c,max}$ on layer number in cuprates within the preformed pair framework.

Findings

$T_{c,max}$ peaks at $n=2$, $n=3$, or beyond depending on parameters.

Increasing layers initially raise $T_{c,max}$ due to lighter pairs.

Beyond a certain layer number, kinetic energy weakens pairs, reducing $T_{c,max}$.

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.