Proximity-Induced Nodal Metal in an Extremely Underdoped CuO${}_2$ Plane in Triple-Layer Cuprates

Abstract

ARPES studies have established that the high-$T_c$ cuprates with single and double CuO${}_2$ layers evolve from the Mott insulator to the pseudogap state with a Fermi arc, on which the superconducting (SC) gap opens. In four- to six-layer cuprates, on the other hand, small hole Fermi pockets are formed in the innermost CuO${}_2$ planes, indicating antiferromagnetism. Here, we performed ARPES studies on the triple-layer Bi${}_2$Sr${}_2$Ca${}_2$Cu${}_3$O${}_{10+\hat{I}´}$ over a wide doping range, and found that, although the doping level of the inner CuO${}_2$ plane was extremely low in underdoped samples, the $d$-wave SC gap was enhanced to the unprecedentedly large value of $\hat{I}{”}_0\sim$100 meV at the antinode and persisted well above $T_c$ without the appearance of a Fermi arc, indicating a robust ``nodal metal''. We attribute the nodal metallic behavior to the unique local environment of the inner clean CuO${}_2$ plane in the triple-layer cuprates, sandwiched by nearly optimally-doped two outer CuO${}_2$ planes and hence subject to strong proximity effect from both sides. In the nodal metal, quasiparticle peaks showed electron-hole symmetry, suggesting $d$-wave pairing fluctuations. Thus the proximity effect on the innermost CuO${}_2$ plane is the strongest in the triple-layer cuprates, which explains why the $T_c$ reaches the maximum at the layer number of three in every multi-layer cuprate family.