Comment on "Distinct Behaviors of Inner and Outer CuO$_2$ Planes in Quadruple-Layer Cuprate (Cu,C)Ba$_2$Ca$_3$Cu$_4$O$_{11 + \delta}$"

Abstract

In a recent Letter, Sun et al. report photoemission spectroscopy measurements on the four-layer cuprate (Cu,C)Ba2Ca3Cu4O11 (CuC-1234) in which they resolve two superconducting gaps associated with the inner (IP) and outer (OP) CuO2 planes. CuC-1234 has a Tc as 117 K in a sample previously structurally characterized using neutron powder diffraction. From the Luttinger sum, the beta-band of the IP was found to be heavily underdoped (p~0.07) while the OP alpha2 bonding band was strongly overdoped (p~0.25). Each revealed a gap with very different momentum and temperature dependences. A large gap on the beta band was found to close at the bulk Tc, while a smaller gap on the alpha2 band closed at 70 K. Such two-gap behavior would indicate weak-coupling between the IP and OP, resulting in a second gap-opening temperature, Tc2, and implying a two-step development of the superfluid density on cooling, first on the IPs then on the OPs. Here, we point out that the observed values of Tc and Tc2 are fully consistent with a long-standing correlation of Tc with a bond-valence sum parameter, V+, calculated from the crystallographic bond lengths. This suggests that Tc2 in the OP is entirely consistent with the local structure of the OP where the value of V+(OP) is reduced by the presence of the apical oxygens and Tc2 reduced accordingly. It is as though two largely decoupled superconductors are present in the single 1234 compound and their individual pairing temperatures are determined by their local nearest-neighbour structure, reflecting the very short-range physics.