Description
The superconducting transition temperatures ($T_{\mathrm{c}}$'s) of trilayer or quadruple-layer cuprates typically surpass those of single-layer or bilayer systems. However, the lack of direct electronic-structure and superconducting-gap measurements in optimal-$T_{\mathrm{c}}$ quadruple-layer cuprates has impeded a comprehensive understanding of the origin of the enhanced $T_{\mathrm{c}}$ in multilayer systems. In this study, using angle-resolved photoemission spectroscopy, we investigate the quadruple-layer cuprate (Cu,C)Ba$_2$Ca$_3$Cu$_4$O$_{11+\delta}$ (CuC-1234) with a high $T_{\mathrm{c}}$ of 110 K, and resolved distinct superconducting gap behaviors between the inner CuO$_2$ planes (IPs) and outer CuO$_2$ planes (OPs), in contrast to that reported for trilayer cuprates. OPs develop their own superconducting gap and superconducting coherence peak at a temperature much lower than the $T_{\mathrm{c}}$ of the material, while the large pairing strength and phase coherence concurrently emerge at the underdoped IPs at $T_{\mathrm{c}}$. Our findings suggest that CuO$_2$ planes free of apical oxygen can have significant contribution to superconductivity up to 110~K in multilayer cuprates, 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.
