Planar hole-doping concentration and effective three-dimensional hole-doping concentration for single-layer high-$T_c$ superconductors

TL;DR

This paper introduces two doping concentration metrics, $P_{pl}$ and $P_{3D}$, revealing a universal dome-shaped relationship between $T_c$ and $P_{3D}$ with a consistent optimal doping level across single-layer high-$T_c$ superconductors.

Contribution

It proposes the effective three-dimensional hole-doping concentration $P_{3D}$ as a key parameter for understanding superconducting properties, unifying behavior across different materials.

Findings

$T_c$ shows a universal dome shape when plotted against $P_{3D}$.

Optimal doping concentration at $P_{3D} \\sim 1.6 \\times 10^{21}$ cm$^{-3}$.

$P_{3D}$ effectively captures the doping dependence of superconductivity.

Abstract

We propose that physical properties for the high temperature superconductors can be addressed by either a two-dimensional planar hole-doping concentration ($P_{pl}$) or an effective three-dimentional hole-doping concentration ($P_{3D}$). We find that superconducting transition temperature ($T_c$) exhibits a universal dome-shaped behavior in the $T_c$ $vs.$ $P_{3D}$ plot with a universal optimal doping concentration at $P_{3D}$ $\sim$ 1.6 $\times$ 10$^{21}$ cm$^{-3}$ for the single-layer high temperature superconductors.