Distinct Behaviors of Inner and Outer CuO_{2} Planes in Quadruple-Layer Cuprate (Cu,C)Ba_{2}Ca_{3}Cu_{4}O_{11+δ}

The superconducting transition temperatures (T_{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_{c} quadruple-layer cuprates has impeded a comprehensive understanding of the origin of the enhanced T_{c} in multilayer systems. In this Letter, using angle-resolved photoemission spectroscopy, we investigate the quadruple-layer cuprate (Cu,C)Ba_{2}Ca_{3}Cu_{4}O_{11+δ} (CuC-1234) with a high T_{c} of 110 K, and resolved distinct superconducting-gap behaviors between the inner CuO_{2} planes and outer CuO_{2} planes, in contrast to that reported for trilayer cuprates. Outer CuO_{2} planes develop their own superconducting gap and superconducting coherence peak at a temperature much lower than the T_{c} of the material, while the large pairing strength and phase coherence concurrently emerge at the underdoped inner CuO_{2} planes at T_{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_{c} in multilayer cuprates.