High Temperature Superconductivity Dominated by Inner Underdoped CuO$_2$ Planes in Quadruple-Layer Cuprate (Cu,C)Ba$_2$Ca$_3$Cu$_4$O$_{11+\delta}$

TL;DR

This study reveals that in quadruple-layer cuprates, high-temperature superconductivity is primarily driven by underdoped inner CuO$_2$ planes, challenging the traditional composite picture and showing superconductivity can occur without apical oxygen at high doping levels.

Contribution

The paper demonstrates that high $T_c$ in multilayer cuprates originates from underdoped inner planes, not outer planes, and that apical oxygen-free CuO$_2$ planes can support high-temperature superconductivity.

Findings

Superconductivity mainly arises from underdoped inner CuO$_2$ planes.

Outer planes are not superconducting at $T_c$.

CuO$_2$ planes without apical oxygen support superconductivity up to 110 K.

Abstract

The superconducting transition temperature ($T_{\mathrm{c}}$) of trilayer or quadruple-layer cuprates typically surpasses that of single-layer or bilayer systems. This observation is often interpreted within the ``composite picture", where strong proximity effect between inner CuO$_2$ planes (IPs) and outer CuO$_2$ planes (OPs) is crucial. Albeit intriguing, a straightforward scrutinization of this composite picture is still lacking. In this study, using angle-resolved photoemission spectroscopy to investigate (Cu,C)Ba$_2$Ca$_3$Cu$_4$O$_{11+\delta}$ (CuC-1234) with a high $T_{\mathrm{c}}$ of 110~K, we found that the OPs are not superconducting at the $T_{\mathrm{c}}$ of the material. Instead, the large pairing strength and phase coherence concurrently emerge at the underdoped IPs, suggesting that the high $T_{\mathrm{c}}$ is primarily driven by these underdoped IPs. Given that the $T_{\mathrm{c}}$ of CuC-1234 is comparable to other trilayer or quadruple-layer cuprates, our findings suggest that the conventional ``composite picture" is not universally required for achieving high $T_{\mathrm{c}}$. More importantly, we demonstrate that CuO$_2$ planes free of apical oxygen can support superconductivity up to 110~K even at a doping level of 0.07 holes per Cu, a level that lies deep in the underdoped regime of single- and bilayer cuprates. These findings provide new insights into the origin of high $T_{\mathrm{c}}$ in multilayer cuprates.